UC-NRLF 


ARITHMETIC 


EUGENE  HERZ 

AND 

MARY  G.  BRANTS 

MANUAL 


PARTS  VII 
AND    VIII 


■otm^K 


ISGO,  CALfF, 


httD://www.archive.ora/details/arithmeticteacheOOherzrich 


ARITHMETIC 


BY 

EUGENE  HERZ 

CERTIFIED    PUBLIC    ACCOUNTANT 
AND 

MARY  G.  BRANTS 

CRITIC    TEACHER,    PARKER   PRACTICE  SCHOOL, 
CHICAGO   NORMAL  COLLEGE 

WITH    THE   EDITORIAL  ASSISTANCE   ^F  i  '       '   - 

GEORGE  GAILEY  CHAAIBERS,  Ph.D. 

ASSISTANT  PROFESSOR  OF  MATHEMATICS, 
UNIVERSITY    OK    PENNSYLVANIA 

THE  JOHN  C.  WINSTON  COMfAN 

PUBLISHERS 

571    MARKET  ST 

SAN  FRANCISCO,  CAL.>c*, 

TEACHER'S  MANUAL 

FOR 

PARTS   VII  AND    VIII 

ADVANCED   LESSONS 


THE  JOHN  C.  WINSTON  COMPANY 
CHICAGO  PHILADELPHIA  Toronto 


Copyright,  1920,  by 
Thh  John  C.  Winston  Company 


Entered  at  Stationers'  Hall,  London 
All  rights  reserved 


etc 


FOREWORD 

Bearing  in  mind  that  a  thorough  knowledge  of  arithmetic 
is  perhaps  more  frequently  the  cause  of  success  in  life  than  is 
any  other  single  factor,  one  can  hardly  overestimate  the 
importance  of  this  subject  to  the  future  welfare  of  the  child, 
nor  can  one  fail  to  reahze  how  great  is  the  responsibility 
which  rests  on  those  whose  duty  it  is  to  provide  for  his  edu- 
cation in  this  branch. 

No  book  or  series  of  books  can  possibly  illustrate  every 
use  to  which  numbers  can  be  put,  but  if  the  principles  under- 
lying their  use  are  properly  taught,  the  child  can  reason  for 
himself  the  proper  application  of  his  knowledge  to  any  given 
problem.  Furthermore,  as  he  must  know  not  merely  how 
to  solve  a  problem,  but  how  to  solve  it  in  the  quickest  and 
simplest  manner,  he  must  know  not  merely  the  various  proc- 
esses, but  their  construction  as  well;  he  must  be  able  to 
analyze  to  such  an  extent  that  when  a  problem  is  presented 
to  him,  he  can  distinguish  the  facts  which  are  relevant 
from  those  which  are  irrelevant,  he  can  separate  the  known 
from  the  unknown,  he  can  arrange  the  known  in  logical  order 
for  his  processes,  and  he  can  use  the  shortest  processes  pos- 
sible. An  attempt  to  give  the  pupil  this  abihty  is  the  motive 
for  this  work. 

The  vehicle  used  to  obtain  the  result  is  a  series  of  pro- 
gressive lessons,  which,  with  ample  practice,  take  the  pupil 
step  by  step  through  the  construction  of  each  process  to  be 
learned,  thus  giving  him  the  opportunity  of  following  the 
teacher's  explanation,  and  of  referring  to  past  lessons  at  any 
time.  In  this  way  the  pupil  who  is  slower  to  grasp  new  ideas 
than  the  average  can  keep  up  with  his  class,  and  every  pupil 
can  at  all  times  refresh  his  memory  on  any  points  which  he 
may  have  forgotten  or  which  may  have  escaped  him  in  the 
classroom,  and  which  have  so  often  been  lost  to  him  forever. 

4G4G70 


The  time-saving  methods  used  by  the  most  expert  arithme- 
ticians are  introduced  as  part  of  the  routine  work;  thus, 
these  become  a  part  of  the  child's  general  education  without 
any  special  effort  on  his  part. 

It  is  not  intended  that  the  lessons  or  definitions  are  to  be 
learned  verbatim,  any  more  than  it  is  intended  that  the 
examples  given  are  to  be  memorized;  both  are  there  for  the 
purpose  of  showing  the  pupil  the  reason  for,  and  the  applica- 
tion of,  the  processes,  and  the  exercises  are  there  to  give 
him  practice  and  to  test  his  knowledge  of  what  he  has  learned. 

The  exercises  are  prepared  in  such  manner  that  they  form 
an  automatic  and  continuous  review  of  what  has  been  learned, 
but  further  review  work  is  given  at  regular  intervals. 

The  series  consists  of  Three  Books  and  Teacher's  Manuals, 
as  follows: 

Primary  Lessons Parts    I    and    II.     (Teacher's 

Manual  only.) 

Elementary  Lessons. .  .  .  Parts  III  and  IV.  (With  Manu- 
al for  the  Teacher.) 

Intermediate  Lessons. . .  Parts  V  and  VI.    (With  Manual 

for  the  Teacher.) 

Advanced  Lessons Parts   VII    and   VIII.      (With 

Manual  for  the  Teacher.) 

The  first  two  parts  are  so  arranged  in  the  Teacher's  Manual 
that  the  lessons  and  exercises  can  be  given  largely  as  games, 
pla3^  work,  number  stories,  in  language  work,  etc.,  all  used 
more  or  less  incidentally,  till  the  child  is  gradually  prepared 
for  work  requiring  an  increasing  degree  of  conscious  effort. 

The  work  contained  in  each  of  the  eight  parts  is  that 
which  is  usually  taught  in  the  corresponding  grade,  and  it  is 
recommended  that  this  routine  be  followed.  However,  spe- 
cial provision  has  been  made  for  such  variations  in  the 
grading  as  are  required  in  some  localities,  by  means  of  a 
series  of  notes  in  the  Teacher's  Manuals  which  enable  the 
teacher  to  follow  efther  method  with  equal  facility. 


GENERAL  NOTES  FOR  THE  TEACHER 

1.  Read  the  foreword  carefully. 

2.  Follow  the  detailed  notes  for  each  lesson. 

3.  Each  lesson  is  to  be  thoroughly  demonstrated,  explained 

and  discussed  in  the  classroom  before  being  used  by 
the  pupil  for  study  and  reference.  The  time  required 
for  each  lesson  depends  on  the  ability  of  the  class.  Be 
thorough. 

4.  In  demonstrating,  use  the  objects  of  the  pupil's  environ- 

ment for  concrete  material,  and  let  him  have  first-hand 
experience. 

5.  Illustrate  every  essential  point  on  the  blackboard. 

6.  Do  everything  possible  to  make  the  recitations  interesting 

and  enjoyable. 

7.  Introduce  the  competitive  spirit  wherever  possible. 

8.  Remember  that  proficiency  in  arithmetic  can  be  analyzed 

as  resulting  principally  from  these  three  factors: 

(a)  A  thorough  knowledge  of  the  various  processes  and 

methods. 
(6)  The  ability  to  select  the  process  or  method  most 

applicable  to  the  given  problem, 
(c)  The  elimination  of  all  unnecessary  work. 

9.  Make  the  pupil  realize  that  a  thorough  knowledge  of 

arithmetic  will  be  of  great  value  to  him  throughout 
his  life. 

10.  Before  beginning  the  year's  work,  make  a  careful  survey 
of  the  topics  to  be  covered,  giving  due  consideration 
to  the  Notes  Regarding  Grading  in  the  Teacher's 
Manuals;  then  plan  your  schedule  so  that  you  will  not 
have  to  slight  over  some  of  the  later  work  on  account 
of  lack  of  time. 


CONTENTS 

PART  VII 

LESSON 

NUMBER  PAGE 

Denominate  Numbers 

1.  Reduction 3 

2.  Reduction  of  Fractional  Denominate  Numbers 5 

3.  Addition  of  Denominate  Numbers 5 

4.  Subtraction  of  Denominate  Numbers 5 

5.  Multiplication  of  DenomiisTate  Numbers 5 

6.  Division  of  Denominate  Numbers 5 

7.  Measuring  Land 7 

8.  Paper  Measure 9 

9.  Printers'  Type  Measure 9 

10.  Legal  Weights  of  a  Bushel  (In  Pounds) 10 

11.  Special  Working  Units 12 

Fractions 

12.  Compound  and  Complex  Fractions 12 

Multiplication 

13.  Cross  Multiplication 13 

Time  and  Wages 

14.  How  Wages  Are  Figured 13 

15.  Transposition  in  Figuring  Wages 14 

Mensuration 

16.  The  Circle 15 

17.  The  Ratio  of  the  Circumference  to  the  Diameter.  ...  15 

18.  Finding  the  Area  of  a  Circle 16 

19.  Finding  the  Area  of  the  Surface  of  a  Right   (Rect- 

angular) Prism 17 

20.  Finding  the  Area  of  the  Surface  of  a  Cylinder 18 

21.  Cutting  Material  to  Avoid  Waste 19 

22.  Finding  the  Volume  of  a  Cylinder 19 


LESSON 

NUMBER  PAGE 

Percentage 

23.  Stjucessive  Trade  Discounts 21 

24.  Finding  the  Gross  Amount  When  the  Rates  of 'Discount 

AND  THE  Net  Amount  Are  Given 21 

25.  Insurance 22 

26.  Commission  and  Brokerage 24 

27.  Taxes 25 

28.  Computing  Interest  When  There  Are  Partial  Payments  .  25 

29.  Finding  the  Principal  When  the  Time,  Rate,  and  Interest 

Are  Given 26 

30.  Finding  the  Time  When  the  Principal,  Rate,  and  Interest 

Are  Given 26 

31.  Finding  the  Rate  When  the  Principal,  Time,  and  Interest 

Are  Given 26 

32.  Transposition  in  Figuring  Interest 27 

33.  Compound  Interest 27 

Accounts 

34.  Savings  Bajjk  Accounts 28 

35.  Bank  Accounts  which  Are  Subject  to  Check 29 


CONTENTS 
PART  vm 

LESSON 

NUMBER  Notation  and  Numeration  page 

1.  The  Higher  Periods 3 

Denominate  Numbers 

2.  Table  of  Circular  Measure 4 

3.  Longitude  and  Time 4 

4.  Standard  Time  in  the  United  States 7 

5.  The  International  Date  Line 7 

6.  The  Metric  System 8 

7.  Foreign  Money 9 

Powers  and  Roots 

8.  What  Powers  Are — Squaring  and  Cubing 11 

9.  What  Roots  Are 12 

10.  How  to  Extract  the  Square  Root.     (Integers) 12 

11.  How    TO    Extract    the    Square    Root.      (Decimals    and 

Fractions) 12 

12.  How  to  Extract  the  Square  Root  by  Factoring 13 

Equations 

13.  Numbers  and  Quantities  Represented  by  Letters 15 

14.  Solving  Equations.     (Adding  and  Subtracting) 15 

15.  Solving  Equations.     (Multiplying  and  Dividing) 15 

Mensuration 
IG.  Right  Triangles 15 

17.  Isosceles  and  Equilateral  Triangles 16 

18.  Similar  Triangles 17 

19.  Table  of  Angular  Measure 17 

20.  Measuring  the  Length  of  Arcs  and  the  Area  of  Sectors 

of  Circles 18 

21.  Pyramids 19 


Lesson 

number  i'ace 

22.  Cones 20 

23.  Frustums  (for  Surface  Work  Only) 21 

24.  Spheres 22 

Graphic  Charts  and  Meters 

25.  Graphic  Charts 23 

26.  Meters 24 

Percentage 

27.  Interest  on  Installment  Accounts 25 

28.  Bank  Discount 26 

29.  Mortgages  and  Bonds 26 

30.  Corporations  and  Their  Capital  Stock 27 

31.  Rate  of  Income  (Yield)  on  Stocks  and  Bonds  Bought  at 

A  Premiltm  or  Discount 28 

32.  Insurance 29 

Partnership 

33  Division  of  Profits  and  Losses 31 


TEACHER'S    MANUAL 


ADVANCED  LESSONS 

PART  VII 
AN  INTELLIGENCE  TEST 

This  set  of  test  questions  will  aid  you  in  grouping  your 
pupils  properly,  in  determining  who  are  the  weak  ones  and 
in  checking  the  results  of  your  efforts.  Defective  hearing 
and  sight  will  also  be  disclosed  thereby. 

Make  a  tabulation  of  the  number  of  problems  attempted, 
the  number  correctly  solved,  and  the  percentage  attained 
by  each  child,,  and  keep  it  for  future  comparison.  (Average 
the  per  cent  attempted  and  the  per  cent  solved  of  those 
attempted;  viz.:  8  attempted  out  of,  10  =  80%;  7  solved 
out  of  8  attempted  =  87i%;  average  83|%.) 


Name 

Beginning  of  Year 

Middle  of  Year 

End  of  Year 

Attempted 

Solved 

% 

Attempted 

Solved 

% 

Attempted 

Solved 

% 

Adams,  Bessie 

8 

7 

83f 

Do  not  give  the  pupils  the  result  of  the  test,  nor  show 
them  directly  wherein  they  failed,  but  help  each  group  in 
its  weak  subjects  without  permitting  them  or  the  others  to 
realize  what  you  are  doing. 

At  the  end  of  the  first  half  of  the  school  year  give  the 
same  test  again  and  compare  the  results;  repeat  again  at 
the  end  of  the  school  year.  If  you  desire,  the  test  may  be 
given  more  frequently. 

(VII-1) 


Kow  to  %Jve  tlie  test: 

Write  the  first  nve  problems  (properly  numbered)  on  the 
board  during  the  pupils'  absence  and  keep  them  covered 
until  the  proper  moment  designated  hereafter. 

When  ready  to  begin  the  test,  provide  them  with  paper 
and  read  the  second  five  problems  to  the  pupils  very  slowly 
and  let  them  make  such  memoranda  thereof  as  they  will. 
Give  them  the  number  of  each  problem  as  you  read  it. 

Tell  them  they  are  to  number  their  answers  to  correspond 
with  the  problem  numbers. 

Now  remove  the  covering  from  the  board  and  have  them 
begin.    (Those  on  the  board  come  first.) 

Allow  30  minutes  for  the  actual  working  of  the  problems. 

The  Problems: 

The  first  five  to  be  written  on  the  board : 

1.  A  carload  of  coal  consisted  of  24  T.    20%  of  the  coal 

was  sold  to  A  and  30%  to  B ;  what  quantity  would 
C  and  D  each  receive,  if  each  got  ^  of  what  was  left? 

2.  What  will  12^  A.  of  land  cost,  if  4^  A.  cost  $675.? 

3.  Find  the  interest  on  $450.  at  6%  for  123  days. 

4.  A  farm  containing  10  A.  80  sq.  rd.  is  80  rd.  long; 

find  the  perimeter. 

5.  If  a  quarter-section  of  land  costs  $800.,  what  should 

it  be  sold  for  to  gain  40%? 

The  second  five  to  be  read  to  the  pupils: 

6.  James  Brown  received  $363.18  when  he  sold  a  tract 

of  land  for  his  neighbor  for  $12,106.;   what  rate  of 
commission  did  he  earn? 

7.  (.0006  -^  .002)  +  (.06  X  .0055)  =  ? 

8.  Tom  Jones  owned  |  of  a  boat  worth  $6,000.;     Ik? 

sold  i  of  his  share  for  $4,800.;   what  did  he  gain? 

9.  If  $9.75  interest  was  earned  on  $650.  at  6%,  Iiqw 

long  was  the  money  loaned? 
10.  What  number  divided  by  84^  equals  120^? 
(VII-2) 


The  Answers: 

1.            6T.; 

6.           3%; 

2.    $1,875.; 

7.             .30033; 

3.          $9.23; 

8.  $3,000.; 

4.         202  rd.; 

9.          90  da.; 

5.    $1,120.; 

10.    10,182i. 

Until  further  notice,  the  blackboard  drill  should  now  be 
varied  from  day  to  day,  and  should  cover  rapid  addition 
and  subtraction  in  all  the  forms  taught  in  Parts  IV,  V,  and 
VI,  as  well  as  the  use  of  aliquot  parts  in  multiplication  and 
division.  Give  these  four  or  five  minutes  a  day  if  more  tune  is 
not  a,vailable.    Time  tests  should  be  given  frequently. 

Competition  is  a  wonderful  incentive  for  good  work  and 
continued  effort.  Make  use  of  it  by  giving  "class  honors" 
frequently  and  letting  the  children  strive  for  them.  As 
an  example,  you  can  give  the  honor  of  "Class  Denominate 
Number  Expert"  to  the  boy  or  girl  who  has  done  the  best 
work  in  denominate  numbers  after  Lesson  6  is  completed, 
and  so  on  throughout  the  work. 

DENOMINATE  NUMBERS 
Lesson  1 

Let  the  child  make  a  table  each  time  as  far  as  his  work 
carries  him.  Drill  in  sorting-letters-style  till  he  can  identify 
the  numbers  of  import  in  the  work.  Example  1,  is  in  Linear 
Measure;  after  his  talk  on  it,  place  3, 12,  36  (one  at  a  time) 
on  the  board  and  let  him  say:  "3,  the  number  of  feet  in  1 
yard";  "12,  the  number  of  inches  in  1  foot",  etc.;  later, 
just  this:   "36"=  1  yd."  etc. 

The  drill  must  grow  with  the  need  of  the  problems  until 
the  full  table  is  made  by  use  and  learned.  Then  call  for 
memory  work  on  the  tables. 

The  distinction  between  a  simple  and  a  compound 
denominate  number  is  here  studied  for  the  first  time,  and 

(VII-3) 


this  distinction  must  be  made  clear  to  the  pupils.  Compare 
with  formation  of  compound  words  which  he  knows,  as 
steamboat,  railroad. 

Let  him  create  some  compound  denominate  numbers  that 
you  may  be  enabled  to  see  that  he  understands  that  the 
several  parts  thereof  must  come  from  the  same  table. 

Make  the  child  realize  which  is  the  basic  unit  in  each 
example. 

Reduction  to  smaller  and  to  larger  denominations  should 
be  presented  co-relatedly  as  each  of  these  processes  is  more 
easily  understood  by  reason  of  the  other.  Explain  carefully 
the  method  of  proving  by  approximation,  and  use  frequently. 
It  will  satisfy  the  children. 


Exercise  2 — Written. 

Answers: 

1.        17  ft.;         5.       49  pt.; 

9. 

98  mo.; 

2.      212  in.;         6.  7,580  min.; 

10. 

50  qt.; 

3.          7pt.;         7.        70  oz.; 

11. 

90  in.; 

4.      157  qt.;         8.        92  in.; 

12. 

14  qt. 

Exercise  3— Written. 

Answers: 

1.    3  hr.  30  min.; 

2.     4  da.  12  hr.  20  min.; 

3.  21yd.  6  in.; 

4.     6  gal.  1  qt.  1  pt.; 

5.     3  pk.  1  qt.  1  pt.; 

6.     6bu.  1  pk.  2  qt.  (dry); 

Ibbl.  19  gal.  (liquid); 

7.     3  hr.  15  min.; 

8.     6  da.  7  min. ; 

.      9.  15  lb.  6  oz. ; 

10.     6  sq.  yd.  8  sq.  ft.  38  sq.  in. 

(VII-4) 

Lesson  2 

This  lesson  covers  a  very  important  and  frequently 
neglected  phase  of  reduction,  and  offers  the  opportunity  of 
introducing  examples  in  every  conceivable  form. 

In  reducing  to  smaller  denominations  which  are  two  or 
more  denominations  apart,  as  for  instance,  ^  yd.  to  inches, 
let  the  pupils  carry  the  work  through  each  denomination  in 
this  manner:  iyd.  =  ift.;  ^ft.  =  6  inches;  but  demonstrate 
also  that  as  there  are  36  inches  in  a  yard,  ^  yd.  =  6  inches. 

Exercise  6 — Written. 
Answers: 

11.  i  yd.; 

12.  ^  pk.; 

13.  5i    gal.; 

14.  J    yd.; 

15.  I    gal.; 

16.  U  hr.; 

17.  f    sq.  yd.; 

18.  1      qt.  1  pt.; 

19.  1      ft.  4  in.; 

20.  9      doz. 

Lessons  3,  4,  5,  and  6 

These  lessons  cover  work  similar  in  nature  to  that  which 
the  pupils  have  had  in  previous  Parts,  excepting  that  numbers 
of  three  or  more  denominations  are  now  used.  Drill  on  barrel 
and  hogshead;  also  on  square  rods,  acres  and  square  miles 
as  these  denominations  have  not  previously  been  used. 

Exercise  7— Written.  Call  for  Proofs. 

Answers: 

1.  $56.10;  3.  789iicwt.; 

2.  $3.00;  4.     46fT.; 

(VII-5) 


1. 

4i    ft.; 

2. 

31    pk.; 

3. 

3t^  pk.; 

4. 

H   hr.; 

5. 

4i    da.; 

6. 

12i    ft.; 

7. 

5f   yd.; 

8. 

6Ada.; 

9. 

8i    ft.; 

10. 

3|    bu.; 

5.  $37.38; 

9. 

6iyd.; 

6.  $50.88; 

10. 

104  yd.; 

7.  $27.84; 

11. 

$66.60; 

8.     17iyd.; 

12. 

$50.30. 

$10.40; 

Exercise  8 — Written. 

Call  for  Proofs. 

Answers : 

1.       1  hhd.  1  bbl.  29igal.; 

2.       2  mi.  259rd.  4iyd.; 

3.       6gal.  2qt.  1  pt.; 

4.     11  bu.  1  pk.  6qt.; 

5.     20  sq.  yd.  6  sq.  ft.  72  sq.  in. 

i 

$74.60; 

6.      3gr.  7|doz.; 

$1.31; 

7.  946  yd.; 

8.     11  hr.  55  min. 

Exercise  9— AVritten. 

Call  for  Proofs. 

Answers: 

1.    248  da.  23  hr.; 

2.      41  hhd.  1  bbl.; 

3.  $245.50; 

4.         1  mi.  316  rd.  2  yd.; 

5.      87  rd.;      $9.57; 

6.       75  cu.  yd.  18  cu.  ft.  576  cu, 

.  in. 

Exercise  11 — Written.  Call  for  Proofs. 

Answers: 

1.  43  da.  23  hr.  55  min.; 

2.  12  mi.  160  rd.  3  yd.; 

3.  40  cu.  yd.  18  cu.  ft.  869  cu.  in.; 

4.  2  sq.  ft.  8  sq.  in.; 

(VII-6) 


5.  8T.  lOcwt.  50  1b.; 
<3.  4hhd.  Ibbl.  7  gal.; 
7.  176yd.; 

8.  Side  =  4  yd.  2  ft.  6  in.; 
Area  =  23^  sq.  yd.; 

9.  IT.  11  cwt.  70  1b. 

Exercises  10  and  12  afford  an  opportunity  of  clinching  the 
tables,  for  their  apphcation,  and  for  the  development  of 
speed.  Try  to  keep  the  lessons  brisk.  The  slow  ones  will 
struggle  to  keep  pace  with  the  others.  Work  hard  for  quick 
identification  of  number  to  special  application  given. 


Exercise  13 — Written. 

Answ( 

3rs: 

1. 

864  pieces; 

11.  $63.50  Total  Cost; 

2. 

4  sq.  rd. ; 

50^  Saved; 

3. 

|ft.; 

12.  Hay  is  more  profitable; 

4. 

143  lengths; 

Difference  $1,920.00; 

5. 

30  times; 

13.  1,890,000  magazines; 

6. 

$1.17; 

14.      40  tools; 

7. 

.125; 

15.1,125  lb.; 

8. 

$3,180.00; 

16.     280  packages; 

9. 

$15.00  Profit; 

17.     215  plants; 

50%  Profit; 

18.       32  jars; 

10. 

100  bu.; 

19.         8  hr.  30  min. ; 

$1.00  per  bu. 

;  20.      40  sq.  yd. 

Give 

your  ''class  honor"    now   for   denominate  number 

work. 

Lesson  7 

Not  too  much  time  should  be  devoted  to  this  lesson;   the 

principal  points  to  be  brought  out  are: 

(a)  That  a  township 

is  a  6-mile  square  containing  36 

sq.  mi.; 

(VII-7) 

(6)  That  a  section  is  a  1-mile  square  containing  1  sq.  mi. 

or  640  acres, 
(c)  That  each  section  is  divided  into  four  quarters. 

Let  the  children  locate  farms  at  sight,  as: 


SEC.  12. 


A 

M 

B 

N 

C 

D 

E 

F 

Q.      Locate  M. 

Ans.  M  =  N.  i  of  N. 
E.  i  of  Sec.  12. 

Q.      Locate  E. 

Ans.  E  =  S.W.iof  S. 
E.  i  of  Sec.  12. 

Call  for  number  of 
acres  in  each. 

Call  for  miles  of  fenc- 
ing required  for  each. 

Call  for  rods  of  fenc- 
ing required  for  each. 


2. 
3. 

4. 


Exercise  15 — Written. 
Answers: 

1.  ^  section; 
i  section; 
■g-  section; 
^  quarter-section; 
Yff  section; 
i  quarter-section; 

5.  1  mi.  by  ^  mi.; 
320  rd.  by  160  rd. 

6.  i  mi.  by  ^  mi. ; 
160  rd.  by  160  rd. 

7.  i  mi.  by  \  mi. ; 
160  rd.  by  80rd.; 

8.  i  mi.  by  ^  mi- ; 
80  rd.  by  SOrd.; 


10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 


20  acres; 
7^  acres; 


5  acres; 
2i  acres; 
2^  acres; 
2^  acres; 
160  rods; 
1  mile; 
20  rods; 
320  rods; 
4  miles; 

21.  80  rods; 

22.  320  rods. 


20  rods; 


(VII-8) 


Lesson  8 

This  lesson  not  only  familiarizes  the  pupils  with  the  cus- 
toms governing  the  purchase  of  paper,  but  offers  invaluable 
work  in  the  practical  application  of  ratio  and  proportion. 

Place  a  22"  X  34"  oblong  on  the  board  and  cut  it  into  two 
17"  X  22"  oblongs  to  show  the  ratio. 


Exercise  17— Written. 

Answers: 

1.      $7.20; 

6.     $12.00; 

2.      88  lb.;  Ratio 

=  2; 

7.  $400.00;* 

3.    144  lb.;  Ratio 

=  i; 

8.       $3.60; 

4.      $1.62; 

9.     $30.00; 

5.  $222.60; 

10.  $228.00. 

Lesson  9 
This  lesson  is  of  great  benefit  in  three  distinct  ways: 

1st.  It  affords  abundant  drill  in  multiplication  and 
division. 

2d.  It  teaches  a  subject  which  will  be  of  considerable 
value  to  the  child  at  all  times. 

3d.  And  not  least.  It  teaches  concentration  and 
analysis,  as  the  child  must  concentrate  and 
analyze  to  ascertain  the  number  of  ems  of 
different  sizes  of  type  to  an  inch. 

This  lesson  can  be  made  very  interesting  by  having  the 
children  bring  newspapers,  magazines,  and  books  to  school, 
and  have  them  measure  the  various  sizes  of  type  faces  and 
pages  for  the  number  of  points,  picas,  and  ems.  Let  them 
measure  their  school  books;  they  will  enjoy  it  immensely. 


*  In  this  example  the  size  of  the  sheet  has  no  bearing  on  the  answer; 
(4  T.  @,  5^  per  lb.  =  $400.00).  Note  how  many  of  the  pupils  realize 
this  from  a  reading  of  the  example. 

(VII-9) 


Exercise  19 — Written. 


Answers: 

1.      468  points; 

5.  1,728  ems  12-point; 

39  picas; 

6,912  ems    6-point; 

2.         8iin.; 

6.        42  picas  wide; 

49^  picas; 

54  picas  long; 

3.  1,602  points  long; 

7.  1,512  ems; 

162  points  wide; 

8.          8  in.  long; 

133^  picas  long ; 

9.          4  columns; 

13i  picas  wide; 

1,512  ems  per  colmnn 

4.        81  ems  in  1  line; 

6,048  ems  per  page; 

108  ems  long; 

10.         8fin.; 

8,748  ems  per  page; 

52  picas. 

Lesson  10 

Note  Regarding  Grading. 

Where  Lesson  10  has  been  taught  in  the  fifth  year,  it  must 
nevertheless  now  be  given  as  review  work. 

The  pupils  should  be  familiar  with  the  legal  weights  (for 
their  state)  of  a  bushel  of  the  more  common  farm  products. 
This  lesson  may  be  given  in  several  installments  to  facilitate 
memorization.  Bottles  of  grain  of  the  different  kinds  should 
be  used  to  help  the  children  familiarize  themselves  with 
the  several  varieties;  let  them  handle  the  grain  and  learn 
the  weights  at  the  same  time.    Test  them  occasionally. 

The  tables  with  which  this  subject  closes  are  those  used 
in  certain  professions  requiring  a  technical  education  and 
need  not  be  learned,  but  the  pupils  should  be  made  familiar 
with  their  names  and  their  uses. 

Note  Regarding  Grading. 

Where  it  is  required  that  work  on  the  Table  of  Circular 
Measure  be  given  in  the  seventh  year,  Lesson  2  (including 
Exercises  4  and  5)  of  Part  VIII  should  now  be  given. 

(VII-10) 


Note  Regarding  Grading. 

Where  it  is  required  that  work  in  foreign  money  be  given 
in  the  seventh  year,  Lesson  7  (including  Exercise  14)  of 
Part  VIII  should  now  be  given. 

Exercise  21 — Oral  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 

Exercise  22 — Written  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 


permitting. 

Answers: 

1. 

June  6,  1919; 

21. 

366,097 

$255.78; 

22. 

598,853 

2. 

3,880  bd.  ft.; 

23. 

27,293 

3. 

$600.00; 

24. 

199,017 

4. 

$54.88; 

25. 

239,844 

5. 

29iV%; 

26. 

34,360 

6. 

5i  min.  per  report; 

27. 

33,304 

12  trips; 

28. 

33,791 

7. 

$21.06; 

29. 

434 

8. 

1  sq.  yd.  7 

sq. 

ft.  49  sq.  in.; 

30. 

639 

9.  5,184  cu.  in.; 

31. 

728 

10. 

3  da.  4  hr. 

45 

min.  30  sec: 

32. 

864 

11. 

434,634; 

33. 

707 

12. 

239,299; 

34. 

901 

13. 

389,096; 

35. 

27,218 

14. 

729,944; 

36. 

22,742 

15. 

189,930; 

37. 

31,434 

16. 

264,977; 

38. 

6,656 

17. 

96,815; 

39. 

19,285 

18. 

615,138; 

40. 

29,580 

19. 

463,108; 

41. 

29,029 

20. 

155,970; 

(VII-11) 

42. 

37,666 

Lesson  U 

This  interesting  and  useful  lesson  should  be  thoroughly- 
mastered.  It  constitutes  a  thorough  test  of  the  pupil's 
knowledge  of  the  proper  application  of  multiphcation  and 
division.  Call  for  equivalents  often,  as:  2  lamps  for  8 
hours,  or  1  lamp  for  16  hours,  or  4  lamps  for  4  hours,  etc. 


Exercise  24 — Written. 

Answers: 

1.  20  men; 

5.  $3,937.50; 

2.  30  men; 

6.          7hr.; 

3.  50^; 

7.        40  lamps; 

4.  42  hr.; 

8.        60  hr. 

Give  your  "class  honor" 

again  for  denominate  number 

work. 

FRACTIONS 

Lesson  12 
The  subject  matter  of  this  lesson  is  not  new  to  the  pupil; 
only  the  form  is  new,  and  this  should  be  properly  mastered. 
Use  simple  forms.    Let  children  tell  steps  each  time — parts 
first;  then  results. 

Exercise  26 — Written. 
Answers: 

1.  li;         11. 

2.  A;       12. 

3.  1^;        13. 
4i.     I;    .       14. 

5.  2H;         15. 

6.  H;  16. 

7.  H;  17. 

8.  I;  18. 

9.  f;  19. 
10.  li;          20. 

(\TI-12) 


1; 

21. 

62i; 

31. 

H; 

h 

22. 

600i; 

32. 

i; 

34; 

23. 

280; 

33. 

M; 

5i; 

24. 

35; 

34. 

21  . 

3i; 

25. 

h 

35. 

A; 

7  . 

■5"> 

26. 

^; 

36. 

H; 

2|; 

27. 

"SUi 

37. 

2; 

3; 

28. 

i; 

38. 

3. 

i|; 

29. 

A; 

39. 

1; 

2A; 

30. 

9    . 

40. 

li 

MULTIPLICATION 
Lesson  13 

Cross  Multiplication  is  so  useful  in  every  day  life,  regard- 
less of  the  nature  of  one's  occupation,  that  it  should  form 
part  of  the  arithmetical  equipment  of  every  grammar  school 
graduate. 

Use  small  numbers  of  two  orders  at  first  to  demonstrate, 
then  gradually  use  larger  numbers,  but  use  no  numbers  of 
more  than  two  orders  at  any  time.  Follow  the  text  care- 
fully step  by  step. 

Coax  him  to  keep  his  eye  on  the  problem  or  numbers,  to 
encourage  concentration.  Urge  him  to  do  these  very 
promptly. 


Exercise  28 — Written. 
Answers: 


L 

682 

9.  1,092 

17.     1,958 

25. 

1,230 

2. 

483 

10.  1,462 

18.     1,968 

26. 

1,659 

3. 

672 

n.  1,518 

19.     2,584 

27. 

1,302 

4. 

882 

12.      864 

20.     3,528 

28. 

2,883 

5. 

528 

13.  1,376 

21.  $15.70 

29. 

1,455 

6. 

768 

14.      868 

;        22.     1,296 

30. 

4,096 

7. 

1,008 

15.     851 

23.        462 

8. 

1,428 

;        16.  3,038 

TIME  / 
-Le 

;        24.     2,080 

lnd  wages 

SSON    14 

Teach  the  pupils  the  necessity  of  recognizing  aliquot 
parts  of  48  hours  or  of  any  other  weekly  hour  basis. 

In  firfding  a  fraction  of  a  week's  wages,  such  as  If  of  $25- 
the  importance  of  multiplying  43  X  25  and  dividing  by  48, 
rather  than  dividing  25  by  48  and  multiplying  by  43,  is 
great,  both  for  accuracy  and  for  speed. 

(VII-13) 


Exercise  30— Written. 

Answers: 

1.  Adams,  $16.88 

5. 

$7.14; 

Jones,    $24.00 

6. 

40hr.; 

2.  Bailey,     $3.50, 

7. 

37ihr.; 

Davis,     $5.00 

8. 

$36.00; 

3.              $338.00 

9. 

$20.00. 

4,                $18.00 

Lesson 

15 

The  principle  of  transposition,  applied  here  to  the  hours 
worked  and  the  rate  of  wages  when  the  rate  of  wages  is  an 
aliquot  part  of  the  weekly  hour  basis,  should  be  thoroughly 
mastered,  as  other  applications  thereof  appear  later  in  con- 
nection with  other  processes. 


Exercise  32— Written. 

Answers: 

1.    $6.67 

;              6.    $7.33; 

2.    $6.67 

7.  $13.13; 

3.  $18.75 

8.  $25.00; 

4.  $10.19 

9.  $18.38; 

5.    $7.33 

10.     $1.50. 

Give  your  "class  honor 

"  now  for  work  in 

Exercise  33 — Oral  Review 

r. 

More  review  work  of  a  similar  nature  may  be  given,  time 
peimitting.  Time  them.  Then  coax  them  to  ''outrun" 
themselves.    Let  them  try  them  over  and  over  to  wjn. 


Exercise  34 — Written  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 

(VII-14) 


Answers: 
1.  Aug.  14, 1918; 

$398.53; 
2.110,000.; 


3. 

4. 
5. 

6. 

7. 


11. 
12. 
13. 
14. 
15. 
2,030  bd.  ft.;  16. 


661%; 
$9.66; 


$71.05; 

74,fr%; 
48  hr.; 
$2.37; 
69,722; 


8. 

9.394,199 
10.  648,357 


17. 
18. 
19. 
20. 
21. 
22. 
23. 


165,391 
169,745 
202,393 
212,196 
119,188 
146,888 

99,892 
188,889 
193,989 

79,099 
429,969 
207,899 

96,365 


24. 

396,584 

37. 

27; 

25. 

187,532 

38. 

47; 

26. 

104,812 

39. 

34; 

27, 

460,362 

40. 

27; 

28. 

476,672 

41. 

28; 

29. 

246,304 

42. 

34; 

30. 

617,148 

43. 

26; 

31. 

750,984 

44. 

97; 

32. 

4,464 

45. 

34; 

33. 

27 

46. 

24; 

34. 

72 

47. 

36. 

35. 

36 

36. 

28 

If  you  have  not  yet  repeated  the  intelhgence  test  given  at 
the  beginning  of  the  year,  now  is  a  good  time  to  do  so. 

MENSURATION 

Lesson  16 

This  lesson  must  be  thoroughly  clear  to  the  pupils,  other- 
wise the  following  lessons  cannot  be  properly  assimilated. 
Call  on  a  child  to  talk  on  various  things  connected  with  the 
circle  (at  board).  Let  another  tell  some  more.  Who  is 
ahead?  You  will  develop  terms,  recognition  of  relative 
parts  and  English. 


Lesson  17 

The  ratio  3.1416  and  its  designation  "pi"  must  be  firmly 
impressed  upon  the  pupil's  mind.  Train  for  use  of  3y  as 
ratio  at  times.  This  strengthens  on  decimals  and  common 
fractions. 

Also  spare  no  effort  to  help  the  pupil  to  properly  familiarize 
himself  with  the  equation  form.     Always  get  him  to  say 

(VII-15) 


C  =  ttD,  then  work  it. 


R  =  ^- 


D  =  2R.       Let 


E>  =  — ;    XV  --  2> 
him  get  the  habit  of  making  his  own  rules  and  to  work 
by  them,  so  he  gets  the  value  and  joy  out  of  them. 


Exercise  37 — Written. 
Answers: 

1.  2  in.; 

2.  6  ft.;  or,  2  yd.; 

3.  12.5664  yd.; 

4.  6iin.; 

5.  62.832  ft.; 


6.  4  in. ; 

7.  3.1416  yd.;  ^ 

8.  50  yd.; 

9.  2.87  yd.; 

10.  10  yd.  2  ft.  11.8416  in. 


Exercise  38 — Written. 
Answers: 

1.  88  in.; 

2.  28.64  + in.; 

3.  13  in.; 

4.  220  times: 


5.  17.83  in.; 

6.  7  times  (approximately) ; 

7.  20  laps; 

8.  1  lap  and  12  yd. 


Lesson  18 

The  simplicity  of  converting  a  circle  into  a  rectangle  by 
first  changing  it  to  triangles  can  be  so  clearly  demonstrated 
that  this  method  should  be  taught  in  preference  to  the 
slightly  shorter  method  of  ttR^  which  is  not  easily  demon- 
strated and  which  involves  the  process  of  "squaring"  which 
is  more  advantageously  taught  in  Pai't  VIII. 
I  Remember,  the  child  knows  how  to  find  the  area  of  a 
rectangle  and  how  to  find  the  circumference  of  a  circle;  now, 
by  merely  using  ^  the  circumference  as  the  base  of  the 
rectangle  and  the  radius  as  the  altitude,  the  process  is 
identical  to  that  of  finding  the  area  of  the  rectangle. 

Let  the  child  cut  circles  as  indicated  and  have  him  com- 
pare them  to  find  that  the  curved  base  becomes  more  nearly 
straight  as  the  number  of  parts  becomes  greater. 

(VII-16) 


Exercise  40 — Written. 
Answers: 

1.  50.2656  sq.  ft.; 

2.  78.54  sq.ft.; 

3.  113.0976  sq.  in.; 

4.  7,854  sq.  yd.; 

5.  .19635  sq.  in.; 

6.  78.54  sq.  in.; 

7.  176.715  sq.  ft.; 

8.  D  =  14  in.;  Area  =154  sq.  in.; 

9.  Area  of  square  =  196  sq.  in. ; 
Difference  in  areas  =  42  sq.  in.; 
Ratio  11  to  14; 

10.  12.5664  sq.ft.; 

11.  3.1416  sq.  ft; 

12.  9.4248  sq.ft.; 

13.  50.2656  sq.  yd.; 

14.  25.1328  sq.  in.; 

15.  3.1416  sq.ft.; 

16.  154  sq.  in.; 

17.  9f  sq.  in.; 

18.  a  sq.  in. 

Lesson  19 

No  difficulty  of  any  kind  will  be  experienced  with  this 
lesson.  Let  prisms  be  made.  Teach  how  to  add  the  lapels 
for  construction  purposes.  Be  sure  to  keep  all  units  in  square 
measure  and  multiply  by  abstract  numbers  only,  to  obtain 
square  units  in  result. 

Exercise  41 — Written. 
Answers: 

1.  164  sq.  in.;  4.  200  sq.  in.; 

2.  144  sq.  ft.;  5.  112  sq.  yd.; 

3.  96  sq.  in.;  6.     28  sq.  in.; 

(VII-17) 


7. 

800  sq.  in.; 

12. 

433i  sq.  in 

8. 

52  sq.  ft.; 

13. 

150  sq.  in. 

9. 

lOlsq.yd.; 

14. 

128  sq.  in. 

10. 

36ibd.  ft.; 

15. 

152sq.  in.: 

11. 

152  sq.  in. ; 

16. 

1,336  sq.  ft. 

Lesson  20 

Demonstrate  that  the  length  of  the  curved  side  when 
straightened  is  the  same  as  the  length  of  the  circumference 
of  the  base,  and  that  the  width  of  the  curved  side  is  the 
same  as  the  altitude  of  the  cylinder.  Let  cylinders  be  made. 
If  the  children  have  any  difficulty  let  them  handle  the  paper 
cylinders  they  made  and  tell  you  just  what  it  is  they  do 
not  understand  so  that  you  may  help  them.  They  can 
show  it  when  they  cannot  express  it. 


Exercise  42— Written. 

Answers: 

1.  C  =  4  in.; 

7. 

687.58+  sq.  in.; 

2.  32  sq.  in.; 

8. 

Area  =  37.7  sq.  ft.; 

3.     1.27+ in.; 

40.7  sq.  ft.  metal; 

4.     1.27+  sq.  in.; 

9. 

8.25  sq.  in.; 

5.  34.55+  sq.  in.; 

10. 

Area  =  188.5  sq.  in. 

6.  19.1-  in.  by  36 

in.; 

4  tubes. 

Exercise  44 — Written. 

Answers: 

1.       44  sq. 

in.; 

4. 

880  sq.ft.; 

2.  1,120  sq. 

in.; 

5. 

696  sq.  in.; 

3.      133f  sq 

.ft.; 

6. 

27  A's  in  B. 

Lesson  21 

This  lesson  can  be  made  very  interesting  by  having  the 
pupils  prove  their  answers  by  diagrams;   or,  better  still,  by 

(VII-18) 


actually  laying  out  and  cutting  paper  to  correspond  with 
the  arithmetical  result  which  in  every  case  must  have  been 
previously  obtained.  Good  construction  work  may  be 
secured  here.  Teach  him  to  mark  it  off  by  division  each 
time. 

Exercise  46 — Written. 
Answers : 

1.  15  cards;  6.  16  circulars; 
No  waste;  No  waste; 

2.  4  sheets;  1  ream; 
Remainder 2"by 20";  7.  14"  by  21"; 

3.  9  pieces;  9  covers; 
24  sq.  in.  remainder;  8.  32  pages; 

4.  8  letter  heads;  9.  11  letterheads;  (Asshownin 
No  remainder ;  the  example  in  the  lesson) ; 

5.  32  from  a  sheet;  10.  640  pieces. 
16,000  from  a  ream; 

Lesson  22 

If  possible,  have  the  children  make  cylinders  out  of  heavy 
paper. 

Finding  the  volume  of  a  cylinder  is  easily  understood  by 
comparison  with  the  process  of  finding  the  volume  of  a 
prism.  In  both  cases,  the  area  of  the  base  tells  us  how  many 
cubic  units  there  are  in  each  layer,  and  the  altitude  tells  us 
how  many  layers  there  are  in  the  soHd.  Be  sure  that  the 
children  talk  and  understand  "cubic  units  in  each  layer." 

In  its  relation  to  Lesson  18  this  lesson  introduces  but  one 
new  factor,  that  being  altitude. 

If  possible,  demonstrate  Example  6  of  Exercise  48  by  the 
use  of  a  tumbler  of  water.  Ask  the  question:  "Were  the 
water  to  freeze,  what  shape  would  the  piece  of  ice  be?" 
Use  tunnels,  water  pipes,  lead  pencils,  lead  in  the  pencil,  etc. 

VIl-19) 


rercise  48— Written. 

Answers: 

1.  174  cu.  in.; 

6. 

226.20-  cu.  in.; 

2.  315  cu.  yd.; 

7. 

6.28+ cu.  ft.; 

3.  138  cu.  ft.; 

8. 

1,256,640  cu.  ft.; 

4.     65.48+ gal.; 

9. 

3,723.37+ cu.  yd.; 

5.      4.91- gal.; 

10. 

942.48  gal. 

Exercise  49 — Oral  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting,  or  call  for  this  lesson  again  after  a  week  or 
so.  Don't  make  them  feel  the  repeat.  See  if  they  are 
gaining  speed.  Give  the  slower  ones  most  of  the  oral  work 
for  a  short  time. 


Exercise  50 — Written  Review. 


More  review  work  of  a 

similar  nature 

may  be  given,  ti 

permitting. 

Answers: 

1. 

$4.56; 

12. 

42,750 

25. 

4,006,976 

2. 

69%; 

13. 

72,403 

26. 

31,889 

3. 

54sq.yd.  4sq.ft 

.14. 

439 

;      27. 

764,875 

126  sq.  in.; 

15. 

274, 

28. 

420,156 

4. 

125.664  cu.  ft; 

16. 

806 

29. 

499,996 

5. 

1,256.64  sq.ft.; 

17. 

340, 

30. 

169,354 

6. 

432  cu.  in. ; 

18. 

319, 

31. 

448,199 

54  cubes; 

19. 

509, 

32. 

417,016 

7. 

'408  sq.  in.; 

20. 

10,416, 

33. 

84,268 

8. 

3  1b.  3oz.; 

21. 

33,867, 

34. 

86,108 

9. 

129,501; 

22. 

45,136 

35. 

208,056, 

10. 

96,213; 

23. 

840,213 

36. 

257,602, 

11. 

36,113; 

24. 

1,582,880 

37. 

368,982. 

Give  your  "class  honor"  now  for  mensuration  work. 

(VTI-2()) 


PERCENTAGE 

Lesson  23 

Teach  both  methods  of  deducting  successive  discounts, 
and  demonstrate  that  it  is  usually  easier  to  deduct  the  dis- 
counts one  after  the  other  from  the  successive  net  amounts 
when  a  different  set  of  discounts  is  to  be  used  for  each 
example,  and  that  it  is  usually  easier  to  find  and  use  the 
percentage  which  represents  the  net  amount  when  one 
set  of  discounts  is  to  be  used  for  several  examples.  Some 
cannot  see  the  short  cut  until  they  have  tried  both  waj^s. 


tercise  52 — Written. 

Call  for  Proofs. 

Answers: 

1.     $20.30  Discount, 

5. 

$10.80; 

$119.70  Net; 

6. 

$129.60; 

2.     $18.80  Discount, 

7. 

31.6%; 

$61.20  Net; 

8. 

$2.70;  $8.10;  $9.72; 

3.     $38.00  Discount, 

$8.64;  $3.24;  $8.10; 

$162.00  Net; 

9. 

$53.00; 

4.  $126.00  Discount; 

10. 

$62.80. 

$324.00  Net; 

Lesson  24 

Demonstrate   this  lesson   on   the   board   very   carefully, 
using  all  of  the  examples  given  in  the  text. 

Call  for  Proofs. 


8.  $1,336.50  Net;  81%; 

$213.75  Net;  85i%; 

$650.00  Gross;  81%; 
$5,000.00  Gross;  72%; 
$1,000.00  Gross;  87A%; 
$3,645.00  Net;  72A%. 


Exercise  54 — Written. 

• 

Answers: 

1.      $150.00;] 

8 

2.      $118.75; 

9 

3.      m%; 

10 

4.      $250.00; 

11 

5.     $182.40; 

12 

6.      $160.00; 

13 

7.  $1,440.00 Net;  72%; 


(VII-21) 


Lesson  25 
Problem  Project  Suggestions 

When  planning  to  teach  a  given  subject,  motivate  with 
such  work  as  is  found  in  the  child's  activities.  Try  to  find 
something  of  such  interest  to  him  that  the  making  or  doing 
of  that  thing  will  be  quite  real — an  experience  that  is  life 
itself  to  him.  It  may  be  the  planning  and  making  of  a  sled; 
a  garment;  buying  land;  running  a  store,  insurance  office, 
or  bank;  forming  a  corporation;  etc.  Use  the  idea  and  let 
it  include  all  the  activities  that  usually  swing  around  it, 
and  these,  of  course,  will  lead  into  branching  lines.  Go 
steadily  with  the  child,  and  the  subject  will  carry  him  right 
into  life  every  time.  Drills  will  come  in,  and  the  child  will 
be  willing  to  study  because  the  life  project  calls  for  it.  In 
this  way,  interest  will  be  a  constant  factor  and  progress  is 
certain.    Try  it  faithfully. 

The  diagram  on  Page  23  shows  how  a  given  unit  of  the 
child's  experience  may  ramify  and  lead  into  various  collat- 
eral subject  lines  which  constitute  life's  broad  experience. 

In  this  diagram  only  one  kind  of  insurance  on  one  kind 
of  property  has  been  worked  out  in  full.  Each  of  the  other 
kinds  of  property  can  be  worked  out  in  the  same  manner; 
then  each  of  the  other  topics  relating  to  fire  insurance  can 
be  taken  up  in  its  turn.  Next,  we  can  take  up  the  various 
kinds  of  life  insurance;  then  accident  insurance;  and  so  on 
until  every  phase  of  the  subject  has  been  covered  in  detail. 

A  few  moments  in  constructing  a  diagram  of  this  kind  for 
a  problem  project  covering  any  given  subject  will  place  a 
wealth  of  material  at  your  disposal  which  would  otherwise 
escape  your  notice.  Start  with  the  given  subject  and  think 
of  its  principal  characteristics;  then  take  up  the  subdivisions 
of  each  of  these  characteristics.  See  if  there  are  any  collateral 
subjects  that  should  receive  consideration.  Sometimes  the 
children,  themselves,  will  suggest  a  new  line  of  reasoning 
while  the  project  is  under  discussion;  if  so,  make  a  note  of  it. 

(VII-22) 


Diagram  of  Insurance  Problem  Project. 


Insurance 


Fire 


Life 

Accident 
etc. 


Kind  of 
Property 


Policy 


Premium 
etc. 

Straight 

Life 
Endowment 

etc. 


Frame  Building 


Stone  Building 
Merchandise 
Machinery 
Furniture 

etc. 
Length  of  Time 
Coverage 
How  Signed 
Where  Kept 

etc. 
How  Rate  is 

Determined 
How  Computed 
How  Paid 

etc. 


Original  Cost 

Replacement 
Cost 

Depreciation 

Material  Re- 
quired 

Labor  Re- 
quired 

Freight 

Cartage 
etc. 


From  now  on,  the  project  method  can  be  used  frequently 
wherever  possible. 

This  problem  project  will  arouse  a  desire  on  the  pupil's 
part  to  know  all  about  insurance.  Keep  the  work  lively, 
but  correct  at  once  any  misconception  on  the  pupil's  part 
regarding  any  subject. 

(VII-23) 


The  important  things  to  be  brought  out  are. 

(a)  Insurance  is  a  promise  by  an  insurance  company  to 

pay  to  the  insured  a  specified  sum  of  money  in 
case  of  loss  or  injury  of  a  specified  nature. 

(b)  The  written  contract  which  is  given  to  the  insured 

is  the  "pohcy."  The  amount  promised  in  the 
poHcy  is  called  the  ''face"  of  the  policy.  The 
amount  charged  for  taking  the  risk  is  the 
''premium." 

(c)  There  are  many  different  kinds  of  insurance,  but 

those  most  commonly  used  are:  Life,  Accident, 
Fire,  Marine,  Employers'  Liability,  and  Fidelity. 

(d)  The  rate  is  usually  stated  afa  certain  price  per  $100. 

of  insurance,  but  frequently  a  rate  per  cent  is 
stated.  The  rate  depends  entirely  upon  the 
hazards  connected  with  the  risk. 

Exercise  57 — Written. 

Answers: 

1.  $22.50; 

2.  $86.40; 

3.  $26,037.50; 

4.  $4,100.00  premium; 
$10,000.00  paid  to  wife; 

5.  $20,000.00. 

Lesson  26 

This  lesson  presents  no  new  elements,  but  the  meaning 
of  the  several  terms  which  are  used  should  be  clearly  under- 
stood. 

Watch  closely  to  satisfy  yourself  that  the  children  have 
the  ability  to  find  the  amount  of  the  sale  or  invoice.  The 
problem  project  will  give  the  pupils  a  thorough  understand- 
ing of  this  subject. 

(VII-24) 


cercise  59 — Written. 

Call  for  Proofs. 

Answers: 

1.        $17.00  Com.; 

6.  $4,000.00; 

$178.50  Net  Proceeds; 

80  acres; 

2.         $1.20; 

7.        30bbl.; 

3.      $400.00; 

8.      $40.00; 

4.        $64.97; 

9.       500  bbl.; 

5.  $6,275.00  Net  Proceeds;  10.  6f%. 

Lesson  27 

This  lesson  introduces  a  new  form  of  percentage  and 
furnishes  excellent  practice. 

Problem  project  work  can  be  used  to  advantage  here. 

Carefully  explain  the  economic  need  for  taxation  and  its 
application.  The  children  should  read  the  large  numbers 
freely;  encourage  talk  on  big  money.  They  like  it;  it 
teaches  the  use  of  numbers  all  the  while.  The  problem 
project  will  prove  of  great  interest  and  benefit  to  the  pupils. 


Exercise  61- 

-Written. 

Answers: 

1. 

$250.00; 

8. 

$2,437,200.00; 

2. 

$328.90; 

9. 

$4,082.27; 

3. 

$119.25; 

10. 

2i%; 

4. 

$1,500.00: 

11. 

$107.00; 

5. 

$49,617.90; 

12. 

$442.00; 

6. 

ii%; 

13. 

$272.00. 

7. 

$140.35: 

Lesson  28 

Spend  as  much  time  as  is  necessary  to  clearly  demonstrate 
the  illustrated  example.  Use  only  as  many  problems  as  the 
class  needs.  Avoid  drudgery;  it  is  better  to  return  to  the 
subject  in  a  day  or  two  if  necessary. 

(VII-25) 


Exercise  63 — Written. 
Answers: 

1.  Aug.  6,  1918;  $155.00; 

2.  Mar.  5,  1924;    $49.25; 

3.  $1,076.00. 

Note  Regarding  Grading. 

Where  Lessons  29  to  31  have  been  taught  in  the  sixth 
year,  they  must  nevertheless  now  be  given  in  their  entirety 
as  review  work,  with  such  saving  in  time  as  is  made  possible 
by  the  previous  teaching. 

Lesson  29 
Follow  the  method  of  analysis  shown  in  the  text;  i.  e.\ 

Total  Int.-^  Int.  on  $1.  =  No.  of  dollars  in  Principal. 

Total  Int.  4-  Int.  at  1%  =  No.  of  %  in  Rate. 

Total  Int.  -^  Int.  for  1  yr.  =  No.  of  yr.  in  Time. 
This  one  exception  is  to  be  emphasized : 

Total  Amt.-^  Amt.  of  $1.=  No.  of  dollars  in  Principal. 
Make  frequent  use  of  the  formulae  for  the  various  processes. 


Exercise  65— Written. 

Call  for  Proofs 

Answers: 

1.      $400.00 

5.  $2,400.00; 

2.      $540.00 

6.      $400.00; 

3.      $870.00 

7.  $3,400.00; 

.4.  $1,250.00 

8.      $418.80. 

Lessons  30  and  31 
These  lessons  will  be  quickly  understood  and  mastered. 
Exercise  66 — Written.  Call  for  Proofs. 

Answers: 

,    1.  3  mo.;  3.  9  mo.; 

2.  liyr.;  4.  9imo.; 

(VII-26) 


5.  3iyr 

) 

8. 

60  da.; 

6.     Syr. 

2 

mo.; 

9. 

1 

yr.  6  mo. ; 

7.  45  da 

; 

10. 

10 

mo. 

Exercise  68- 

-Written. 

Call  for  Proofs. 

Answers: 

1. 

4%; 

6. 

H%; 

11. 

6%; 

2. 

H%; 

7. 

5%; 

12. 

1  yr.  4  mo.; 

3. 

6%; 

8. 

3%; 

13. 

$612.00; 

4. 

8%; 

9. 

6%; 

14. 

25  yr. 

5. 

4%; 

10. 

4i%; 

Lesson  32 

This  lesson  covers  a  most  valuable  application  of  trans- 
position, and  shows  how  some  difficult  examples  in  interest 
can  be  converted  into  problems  so  simple  that  they  can 
easily  be  solved  without  the  use  of  paper.  The  whole  process 
is  merely  a  device  for  using  the  numerators  of  an  example 
in  cancellation  in  the  most  convenient  order.  Spare  no 
effort  to  teach  this  lesson  properly.  You  will  have  another 
chance  to  see  if  the  child  ''relates"  numbers.  Work  hard  to 
save  him  if  he  does  not  relate  by  this  time  or  he  will  soon 
be  lost. 


Exercise  70- 

-Written. 

Answers: 

1.  $1.85; 

6.  $2.47 

2.  $1.04; 

7.  $0.03 

3.  $2.82; 

8.  $0.64 

4.  $1.30; 

9.  $2.64 

5.  $1.07; 

10.  $0.77 

Lesson  33 

No  difficulty  will  be  experienced  in  connection  with  this 
lesson   as   the   pupils   are   now   thoroughly   famiUar   with 

(VII-27) 


interest  in  its  various  forms  and  applications.  Explain  the 
meaning  of  "semi-annually"  and  "bi-annually"  and  help 
them  to  remember  the  meaning  of  the  prefix  "bi"  by  refer- 
ring to  the  fact  that  a  bicycle  has  two  wheels. 


Exercise  72 — Written. 

Answers: 

1.  $70.92 

2.  $49.45 

3.  $22.67 


4.  $11.17; 

5.  $76.13. 


Note  Regarding  Grading. 

Where  it  is  required  that  bank  discount  be  taught  in  the 
seventh  year,  Lesson  28  (including  Exercises  59  and  60)  of 
Part  VIII  should  now  be  given. 

Give  your  "class  honor"  now  for  percentage  work. 

ACCOUNTS 

Lesson  34 
This  lesson  has  three  distinct  purposes: 

(a)  To  familiarize  the  pupil  with  banking  practice; 
(6)  To  train  the  pupil  in  the  keeping  of  accounts; 
(c)   To  furnish  additional  work  in  compound  interest. 
Therefore,  in  teaching  this  lesson  see  that  each  of  these 
elements  receives  proper  consideration.    Stimulate  the  class 
through  their  own  banking  experience  if  possible.    Excellent 
opportunity  is  here  furnished  for  problem  project  work. 
Demand  careful  and  neat  work  where  ruling  is  required. 

Exercise  74 — Written. 
Answers: 

1.  Balance  $175.00;        3.  Balance  $900.00; 

2.  Interest  63^;  4.  Interest  $16.00. 

(VII-28) 


Lesson  35 

This  lesson  covers  additional  features  in  connection  with 
banking  practice  and  the  keeping  of  accounts,  and  intro- 
duces a  new  element;  i.  e.,  the  reconcilement  of  a  bank 
account.      Cover  each  of  these  three  phases  of  the  lesson. 

A  check  book  should  be  at  hand  and  the  children  should 
see  checks  filled  out  or  should  fill  them  out.  Use  problem 
project  work  here. 

Use  the  word  ''reconcilement"  often  and  urge  the  child 
to  use  it  also;    explain  that  ''reconcilement" 
adjustment  of  a  difference." 

• 
Exercise  76 — Written. 

Answers: 

1.  Balance     $817.27; 

2.  Balance  $1,183.89; 
3. 

Reconcilement  Sept.  30. 

Balance  as  per  Check  Book $817.27 

Checks  Outstanding: 

#17,477  . $321.62 

78 45.00 

366.62 
Balance  as  per  Bank  Statement $1,183.89 

4.  Balance  $18,697.07;  " 

5.  Balance  $20,978.23; 
6. 

Reconcilement  Dec.  31. 

Balance  as  per  Check  Book $18,697.07 

Checks  Outstanding: 

#11,419 $1,347.21 

21 711.48 

22 222.47 

2,281.16 

Balance  as  per  Bank  Statement $20,978.23 

(VII-29)  ■ 


Give  your  "class  honor''  now  for  accounting  work.  Call 
him  the  "Class  Expert  Accountant." 

Note  Regarding  Grading. 

Where  it  is  required  that  powers  and  roots  be  taught  in 
the  seventh  year,  Lessons  8  to  12  (including  Exercises  18 
to  26)  of  Part  VIII  should  now  be  given. 

Note  Regarding  Grading. 

Where  it  is  required  that  equations  be  taught  in  the 
seventh  year,  Lessons  13  to  15  (including  Exercises  28  to  31) 
of  Part  VIII  should  now  be  given. 

Note  Regarding  Grading. 

Where  it  is  required  that  the  right  triangle  be  taught  in 
the  seventh  year,  Lesson  16  (including  Exercises  32  and  33) 
of  Part  VIII  should  now  be  given. 

Note  Regarding  Grading. 

Where  it  is  required  that  pyramids,  cones,  and  spheres  be 
taught  in  the  seventh  year.  Lessons  21  to  24  (including  Exer- 
cises 42  to  50)  of  Part  VIII  should  now  be  given. 

Exercise  77 — Oral  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 

Exercise  78 — Written  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 


nswers: 
1.      $45.33; 

5. 

10%; 

9. 

58,649 

2.      565.488  cu.  in.; 

6. 

60  da.; 

10. 

62,295 

3.    1,884.96  sq.  in.; 

7. 

6%; 

11. 

77,710 

4.      $144.18; 

8. 

$111.70; 

12. 

63,420 

(VII-30) 


13.  188,641, 

22. 

741 

31. 

477,277 

14.  106,820, 

23. 

832, 

32. 

382,763 

15.  329,940 

24. 

947 

;     33. 

612,866 

16.  460,845 

25. 

787 

34. 

120,880 

17.  118,496 

;     26. 

64,126 

;     35. 

109,278 

18.  434,028 

;     27. 

145,439 

;     36. 

773,992 

19.  197,613 

28. 

366,725 

;     37. 

56,104 

20.    430 

29. 

421,884 

21.    604 

30. 

313,093 

General  Review 

All  work  for  general  review  purposes  should  be  selected 
from,  or  based  on,  the  various  exercises  which  constitute 
the  year's  work  in  the  text  book. 

Give  your  review  work  in  three  parts;   viz. : 
(a)  Oral  work  on  principles,  etc. 
(6)  Oral  problems, 
(c)   Written  problems. 

Now  repeat  the  intelligence  test  given  at  the  beginning  of 
the  year,  and  give  each  pupil's  record  for  Parts  V  to  VII 
to  the  teacher  who  will  have  that  pupil  next  year. 

Examination  (If  Desired) 

That  the  examinations  (if  desired)  may  be  a  thorough 
test  of  the  pupil's  knowledge  of  the  work  covered,  and  that 
the  teacher  may  know  what  next  to  undertake,  the  ques- 
tions should  be  selected  from  the  various  exercises  which 
constitute  the  year's  work  in  the  text  book  but  the  teacher 
may  introduce  other  examples  of  a  similar  nature.  Exam- 
inations should  be  held  in  oral  as  well  as  in  written  arithmetic, 
and  should  test  the  pupil's  knowledge  of  both  theory  and 
application. 


(VII-31) 


TEACHER'S    MANUAL 

ADVANCED  LESSONS 

PART  VIII 
AN   INTELLIGENCE   TEST 

This  set  of  test  questions  will  aid  you  in  grouping  \'our 
pupils  properly,  in  determining  who  are  the  weak  ones  and 
in  checking  the  results  of  your  efforts.  Defective  hearing 
and  sight  will  also  be  disclosed  thereby. 

Make  a  tabulation  of  the  number  of  problems  attempted, 
the  number  correctly  solved,  and  the  percentage  attained 
by  each  child,  and  keep  it  for  future  comparison.  (Average 
the  per  cent  attempted  and  the  per  cent  solved  of  those 
attempted;  viz.:  8  attempted  out  of  10  =  80%;  7  solved 
out  of  8  attempted  =  87i%;  average  83f%.) 


\air.e 

Beginning  of  Year 

Middle  of  Year 

End  of  Year 

Attempted 

Solved 

% 

Attempted 

Solved   % 

Attempted 

Solveu   % 

Adams,  Bessie 

8 

7 

83| 

Do  not  give  the  pupils  the  result  of  the  test,  nor  show 
them  directly  wherein  they  failed,  but  help  each  group  in 
its  weak  subjects  without  permitting  them  or  the  others  to 
realize  what  you  are  doing. 

At  the  end  of  the  first  half  of  the  school  year  give  the 
same  test  again  and  compare  the  results;  repeat  again  at 
the  end  of  the  school  year.  If  you  desire,  the  test  may  be 
given  more  frequently. 

(VIII-1) 


How  to  give  the  test: 

Write  the  first  five  problems  (properly  numbered)  on  the 
board  during  the  pupils'  absence  and  keep  them  covered 
until  the  proper  moment  designated  hereafter. 

When  ready  to  begin  the  test,  provide  them  with  paper 
and  read  the  second  five  problems  to  the  pupils  very  slowly 
and  let  them  make  such  memoranda  thereof  as  they  will. 
Give  them  the  number  of  each  problem  as  you  read  it. 

Tell  them  they  are  to  number  their  answers  to  correspond 
with  the  problem  numbers. 

Now  remove  the  covering  from  the  board  and  have  them 
begin.    (Those  on  the  board  come  first.) 

Allow  30  minutes  for  the  actual  working  of  the  problems. 

The  Problems: 

The  first  five  to  be  written  on  the  board : 

1.  If  3|  yd.  of  tapestry  cost  $42.,  what  will  |  yd.  cost 

at  the  same  rate? 

2.  I  sent  $520.  to  an  agent  to  invest  in  land  and  to  pay 

his   4%    commission;     how    many    dollars   were 
invested  in  land? 

3.  Find  the  altitude  of  a  triangle  which  has  a  base  of 

20.6  ft.  and  an  area  of  82.4  sq.  ft. 

4.  What  is  the  ratio  of  the  length  of  the  lines  of  a  2-inch 

square  to  those  of  a  3-inch  square?    What  is  the 
ratio  of  the  areas? 

5.  Mr.   Miller  sold  a  tract  of  land  for  $15,000.   and 

gained  $3,000.;  what  per  cent  of  the  cost  did  he 
gain? 

The  second  five  to  be  read  to  the  pupils: 

6.  Find  the  volume  of  a  rectangular  pyramid  8  in.  high 

and  3  in.  on  each  side  of  the  base. 

7.  Write  a  rule  or  give  a  formula  telling  how  to  find 

the  area  of  a  circle  when  the  radius  is  given. 
(VIII-2) 


8.  Make  three  drawings  of  an  acre  tract  of  land,  show- 

ing different  possible  dimensions. 

9.  Find  the  interest  on  an  $850.  note  for  96  days  at  5%. 
10.  A  field  which  is  four  times  as  long.,  as  it  is  wide,  has 

a  perimeter  of  480  rd. ;  what  are  its  dimensions? 


The  Answers: 

1. 
2. 

S9. ' 
$500.  i 

^    C  X  R         ^, 
7.        2       ^^  ^^  ' 

3. 

8  ft.; 

8.  80  rd.  by  2  rd.; 

4. 

2:3; 

40  rd.  by  4  rd.; 

. 

4:9; 

20  rd.  by  8rd.; 

5. 

25%; 

9.  $11.33; 

6. 

24  cu.  in.; 

10.  Length  192  rd.; 
Width      48  id. 

etc. ; 


The  daily  blackboard  drill  should  include  work  in  rapid 
addition,  subtraction,  multiplication  and  division  in  all  of 
the  forms  taught  in  Parts  IV,  V,  VI,  and  VII.  Let  the 
children  read  numbers  often  besides  writing  them.  Encour- 
age only  one  trial  in  these  drills  to  get  accuracy  and  the  host 
effort  of  the  child.  If  he  is  very  slow  wait  for  him.  Time 
him  frequently  and  show  him  he  is  gaining.  See  whether 
the  slow  child  is  using  the  'Hen"  combinations  or  not. 

Competition  is  a  wonderful  incentive  for  good  work  and 
continued  effort.  Make  use  of  it  by  giving  ''class  honors" 
frequently  and  letting  the  children  strive  for  them.  As  an 
example,  you  can  give  the  honor  of  "Class  Time  Expert" 
to  the  boy  or  girl  who  has  done  the  best  work  in  Standard 
Time  after  Lesson  4  is  completed,  and  so  on  throughout 
the  work. 

NOTATION  AND   NUMERATION 

Lesson  1 
As  we  rarely  use  the  periods  which  are  of  higher  rank  than 
"trillions,"  their  names  and  values  need  not  be  memorized 
but  they  should  be  gone  over  as  a  matter  of  general  interest. 

(VIII-3) 


Use  recent  bond  issues,  expenses  of  the  World  War,  etc., 
to  show  reason  for  learning  billions  and  trillions. 

DENOMINATE   NUMBERS 
Lesson  2 
Note  Regarding  Grading. 

Where  Lesson  2  has  been  previously  taught,  it  must 
nevertheless  now  be  given  as  review  work. 

The  Table  of  Circular  Measure  is  so  simple  that  it  will 
be  very  quickly  learned.  The  point  to  be  emphasized  in 
this  lesson  is  that  there  are  360°  in  every  circumference 
regardless  of  its  size.  To  show  this  plainly,  let  4  children 
draw  4  circles  of  different  sizes  on  the  board.  Demand  care- 
ful drawing.    Remember,  this  work  is  elementary  geometr\'. 


^ercise  5 — Written. 

Answers: 

1.               90°; 

3.        80  miles; 

5,400'; 

4.          1.8  inches; 

324,000"; 

5.  8,115". 

•  2.  9°  55'  45"; 

Lesson  3 

These  are  the  basic  points  to  be  dwelt  on  in  this  lesson: 
(a)  The  location  of  the  equator,  and  the  fact  that  it  is 
a  complete  circumference  dividing  the  earth's  sur- 
face into  the  northern  and  southern  hemispheres. 
(h)  The  location  of  the  Prime  Meridian,  and  the  fact 
that  it,  together  with  the  180th  Meridian,  forms 
a  complete  circumference  dividing  the  earth's  sur- 
face into  the  eastern  and  western  hemispheres. 
(c)   That  the  meridians  of  longitude  are  arcs  running 
north  and  south  but  that  they  indicate  distance 
east  and  west  from  the  Prime  Meridian. 
(VIII-4) 


Harry's  Imaginary  Trips  and  Troubles  will  keep  up  an 
interest  on  account  of  the  real  travel  situations  that  arise. 

The  Table  of  Equivalents  will  be  more  readily  understood 
and  retained  if  a  blackboard  demonstration  is  made,  showing 
by  computation  how  each  of  the  equivalents  is  determined. 
Be  sure  they  know,  15°  15'  15"  of  longitude  corresponds  to 
1  hr.  1  min.  1  sec.  of  time.  From  this  they  can  reason  that 
since  15°  15'  15"  corresponds  to  1  hr.  1  min.  1  sec,  the  number 
of  hours  corresponding  to  any  number  of  degrees  is  deter- 
mined by  finding  the  number  of  times  that  15°  is  contained 
in  the  given  number  of  degrees;  also  that  dividing  any 
number  of  minutes  of  longitude  by  15'  determines  the 
corresponding  number  of  minutes  of  time;  also  that  dividing 
any  number  of  seconds  of  longitude  by  15"  determines  the 
corresponding  number  of  seconds  of  time. 

Work  this  illustration  on  the  board,  first  as  three  separate 
examples,  then  as  a  regular  division  example  in  compound 
denominate  numbers: 

Example:  How  much  time  corresponds  to  32°  5'  12"? 

2  and  2°  rem.  2  8         20f 


15°)  32°              15  (°  '  ") )  32° 

5' 

12' 

30 

' 

2°  =  120';  120'+  5'=  125';         2  = 

=  120 
125 

8  and  5'  rem." 

120 

15')  125' 

5  = 

=  300 
312 

5'=  300";  300"+  12"=  312"; 

300 
12 

m 

15")  312" 
therefore,  32°  5'  12"  corresponds  to  2  hr.  8  min.  20|  sec. 

To  find  the  number  of  °,   ',  or  "  corresponding  to  any 
number  of  hr.,  min.,  or  sec,  we  would  naturally  reverse  the 

(VIII-5) 


process  and  multiply  15°,  15',  or  15"  by  the  number  of 
hr.,  min.,  or  sec,  because  15  of  each  of  these  units  of  longi- 
tude corresponds  to  1  of  each  unit  of  time. 

Example :  How  many  ° ' "  corresponds  to  3  hr.  12  min.  6|  sec? 
15"  3        12         ^ 

x_6i_  X 15  r '  ") 

102";  102"=  r  42";  ^r    W    tW 

48°        1'      42" 
15' 
X   12 
180';  180'+  1'=  181';  181'=  3°  1'; 

IS** 

X     3 

45°;  45°+ 3°=  48°; 

Therefore,  3  hr.  12  nun.  6|  sec.  corresponds  to  48°  1'  42". 

Use  a  globe  and  an  imaginary  sun  to  show  why  the  time 
as  shown  by  the  clock  is  later  the  farther  east  one  goes.  Let 
the  child  who  does  not  understand  turn  the  globe  himself. 
Problem  projects  can  be  used  to  good  advantage  here. 

Exercise  8 — Written. 
Answers: 

1.  40  min.  35  sec; 

2.  87°  36'  30"; 

3.  6:51:45  a.  m.; 

4.  Harry  from  the  East; 
Father  from  the  West; 

5.  Harry  +  75°  3'  15"; 
Father  +  120°  3'  15"; 

6.  (a)  94°  13'  15";  6  hr.  16  min.  53  sec; 
(6)  74°  57'    5";  4  hr.  59  min.  48i  sec; 
(c)   14°    2'  12";  56  min.  8|  sec; 

(VIII-6) 


(d)  92°  58'    0";     6  hr.  11  min.  52  sec; 

(e)  20°  30'  12";     1  hr.  22  min.  i  sec; 

7.  40°  32'  45";     2  hr.  42  min.  11  sec; 

8.  10:19:19  A.  M.; 

9.  52°  30';  East; 

10.  7:50: 18  p.  m.  Wednesday. 

Lesson  4 

This  lesson  is  of  considerable  importance  to  those  pupils 
who  may  later  enter  the  commercial  field;  it  offers  no 
difficulties  and  will  be  quickly  understood.  Problem  projects 
can  be  used  here. 

Mr.  Brown  leaves  Denver  and  wakes  up  in  Chicago;  he 
finds  his  time  all  wrong;  what  change  must  he  make? 
What  about  the  clocks  in  Chicago?  etc  Talk  real  people 
and  their  troubles. 

Give  your  "class  honor"  now  for  time  work. 

Lesson  5 

This  lesson  has  a  very  broadening  effect  on  the  child's 
general  education  quite  separate  and  apart  from  its  value 
as  an  arithmetical  step.    Problem  projects  can  be  used  here. 

If  the  class  does  not  grasp  the  need  of  the  International 
Date  Line  quickly,  use  the  following  for  additional  expo- 
sition. 

Were  it  possible  for  a  traveler  starting,  we  will  say,  from 
Washington,  D.  C,  at  noon  on  Monday  to  travel  westward 
as  rapidly  as  the  earth  rotates  eastward,  he  would  make 
the  entire  journey  around  the  earth  in  24  hours,  during  all 
of  which  time  it  would  be  noon  to  him  as  he  would  remain 
in  exactly  the  same  position  in  relation  to  the  sun.  He  would 
complete  the  journey  at  Washington  24  hours  after  starting, 
which  would  be  noon  on  Tuesday,  but  not  having  passed 
through  a  night,  he  might  well  be  puzzled  to  know  when 
Monday  ended  and  Tuesday  began. 

(VIII-7) 


Exercise  11— Written.  / 

Answers: 

1.  1  hr.  2  min.  6  sec.  difference  in  time;  ' 
15°  31'  30"  difference  in  longitude; 

2.  2  hr.  9  min.  10  sec.  difference  in  time; 
32°  17'  30"  difference  in  longitude; 

3.  4  hr.  4  min.  30  sec.  difference  in  time; 

61°  1'  30"  difference  in  longitude;  ' 

4.  8  hr.  57  min.  15  sec.  difference  in  time; 
134°  18'  45"  difference  in  longitude; 

5.  5  hr.  4  min.  8  sec.  difference  in  time; 
76°  2'  0"  difference  in  longitude; 

6.  0  hr.  16  min.  56i%  sec; 

7.  61°  32'  30"; 

8.  11  hr.  30  min.  42  sec. 

Lesson  6 

(Lessons  6  and  7  may  be  left  till  the  last,  or  made  optional.) 

Note  Regarding  Grading. 

Where  Lesson  6  has  been  taught  in  the  sixth  year,  it  should 
nevertheless  be  given  in  its  entirety  as  review  work,with 
such  saving  in  time  as  is  made  possible  by  the  previous 
teaching. 

In  this  lesson  adhere  strictly  to  the  text.  When  the 
metric  units  and  their  equivalents  in  Linear,  Avoirdupois, 
Dry  and  Liquid  Measures  are  thoroughly  understood,  no 
difficulty  will  be  experienced  with  the  construction  of  the 
metric  system  tables,  but  any  attempt  to  construct  the 
tables  prematurely  must  result  in  endless  confusion  and 
ultimate  failure.  Let  children  try  to  question  each  other 
in  game  fashion — sorting  their  terms  quickly,  etc. 

All  effort  is  now  to  be  limited  to  the  teaching  of  the  values 
of  the  Greek  and  Latin  prefixes:  Myria,  Kilo,  Hecto,  Deka, 
deci,  centi,  and  milli. 

(VIII-8) 


Now  the  pupil  is  to  be  taught  how  to  construct  the 
metric  system  tables  by  combining  the  prefixes  just  learned 
with  the  units  previously  learned.  It  is  desired  that  the 
pupil  should  be  able  to  construct  the  tables — not  memorize 
them. 

Exercise  13 — Written. 


wers: 
1.     1,790.036  m.; 

5.  $32.11; 

2.        642.17  g.; 

6.  48,960  g.; 

3.  10,527.75  1; 

7.     1,713.6  oz., 

107.1  lb. 

4.  $2,947.77; 

Lesson  7 
Note  Regarding  Grading. 

Where  Lesson   7   has  been  previously  taught,  it  should 
nevertheless  be  given  as  review  work. 

An  easy  method  of  memorizing  the  values  of  the  foreign 
coins  in  United  States  money  is  as  follows: 

(a)  An  English  penny  (plural  "pence")  is  worth  a  trifle 

over  $0.02; 
{h)   12  English  pence  (1  shilling)  are  worth  $0.02  X  12 

=  $0.24  +  3  mills  or  $0,243; 
(c)   20  English  shilUngs  (1  pound)  are  worth  $0,243  X 

20  =  $4.86+; 
{(l)  1  French  franc  (100  centimes)  is  worth  5^  less  than 

a  shilling,  or  $0,193; 
(e)   The  Belgian  franc   1 

The  Italian  lira  Each  is  worth  $0,193  the  same 


The  Spanish  peseta 
The  Swiss  franc 


as  the  French  franc. 


The  values  of  the  other  monetary   units  need   not  be 
learned,  as  these  are  given  for  reference  purposes  only. 

Problem  projects  can  be  used — let  different  parts  of  the 
class  represent  different  countries. 

(VIII-9) 


Exercise  14 — Written. 


Answers: 
1.      $243.33 

9. 

£6.; 

17. 

$55.97; 

2.        $23.36 

10. 

£50.  7s 

3d.;     18. 

75  lira; 

3.          $9.85 

11. 

£86.  3d 

.;           19. 

430  peseta; 

4.          $1.42 

12. 

£500.; 

20. 

60  fr.; 

5.  $1,951.26 

13. 

$33.78; 

21. 

500  fr.; 

6.         $9.65 

14. 

$57.90; 

22. 

90  fr. 

7.         $0.15, 

15. 

$15.44; 

8.       $13.18, 

15. 

$86.85; 

Exercise  15 — Written 

Answers: 

1.  9:40  A.  M 

.; 

6. 

$14.60; 

2.        $26.77 

1 

7. 

$1,737.00; 

3.  5  hr.  forward; 

8. 

46  fr.  6  c. 

4.          $2.55 

9. 

$144.75; 

5.      $669.14 

10. 

$386.00; 

$1,362.62 

11. 

Set  it  bad 

c  7  hr. 

$2,433.25 

$4,465.01, 

Give  3'our  ''class  ho 

nor' 

'  now  for  foreign  money  and  met 

system  work. 

Exercise  16 — Oral  Review. 

Train  the  mind  to  run  in  advance  of  speech  pretty  briskly 
here;  let  the  child  add  aloud  while  getting  the  total.  He 
should  see  combinations  of  units  to  shorten  the  work.  Give 
him  more  of  these  problems  if  necessary. 


Exercise  17 — Written  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 

(VIII-10> 


Answers: 

1.  416,000,000,008,016; 

20. 

224,449 

38,164,009,012; 

21. 

494,298 

58,000,006,000,006; 

22. 

206,351 

2.  (a)  10°  6'  50"; 

23. 

137,111 

Q})   309,630"; 

24. 

766,044 

(c)   5,440V; 

25. 

373,576 

3.  1  hr.  1  min.  1  sec. ; 

26. 

538,747 

4.  161°  21'  15"; 

27. 

59,772 

10  hr.  45  min.  25  sec. ; 

28. 

444,225 

5.  2:02  a.m.; 

29. 

398,176 

6.  7:59:58  p.  m.  ; 

30. 

551,002 

7.  1,419.8576; 

31. 

34 

8.  3,345,7901; 

32. 

41 

9.  $278.18; 

33. 

52 

10.  6%; 

34. 

53 

11.  96,896; 

35. 

37 

12.  482,975; 

36. 

64 

13.  64,888; 

37. 

35,260 

14.  333,637; 

38. 

39,030 

15.  206,296; 

39. 

29,047 

16.  442,670; 

40. 

33,000 

17.  96,838; 

41. 

28,508 

18.  312,732; 

42. 

34,201 

19.  702,566; 

POWERS  AND   ROOTS 
Note  Regarding  Grading. 

Where  Lessons  8  to  12  have  been  taught  in  the  seventh 
year,  they  must  nevertheless  now  be  given  in  their  entirety 
as  review  work  with  such  saving  in  time  as  is  made  possible 
by  the  previous  teaching. 

Lesson  8 

The  pupils  must  understand  that  every  number  has  many 
powers,  the  square  and  the  cube  being  respectively  the  powers 

(VIII-11) 


of  the  second  and  third  degrees.  Train  the  eye  to  see  rapidly 
exponents,  indexes,  roots  and  powers  as  the  quick  call  from 
the  teacher  may  demand.  The  terms  are  quickly  learned  in 
this  way. 


Exercise  19 — Written. 


^nsv 

i-'ers: 

1. 

225.; 

15. 

12i; 

29. 

T^; 

2. 

m 

> 

16. 

72i; 

30. 

.015625; 

3. 

1,225.; 

17. 

Hi; 

31. 

A3; 

4. 

15,625.; 

18. 

d'; 

32. 

A; 

5. 

160,000.; 

19. 

X'; 

33. 

201^; 

6. 

2,809.; 

20. 

a'; 

34. 

31; 

7. 

6,561.; 

21. 

32,768.; 

35. 

c"; 

8. 

5,625.; 

22. 

91,125.; 

36. 

m^; 

9. 

676.; 

23. 

884.736; 

37. 

15.625; 

10. 

.6889; 

24. 

1,000,000.; 

38. 

.0144; 

11. 

i; 

25. 

9,261.; 

39. 

1.3924; 

12. 

-5  . 

26. 

151; 

40. 

1^. 

13. 

6i; 

27. 

262,144.; 

14. 

f 

U; 

28. 

110,592.; 

Lesson  9 

Demonstrate  the  meaning  of  square  root  and  cube  root 
on  the  blackboard  by  squaring  and  cubing  simple  numbers 
and  pointing  out  the  roots  and  the  powers. 


Lessons  10  and  11 

Have  hsts  of  perfect  squares  on  the  board  and  let  children 
tell  at  sight  how  many  figures  there  are  in  the  roots.  Give 
plenty  of  time  to  pointing  off. 

As  is  shown  in  the  text,  the  process  of  extracting  the  square 
root  of  a  number  is  the  exact  reverse  of  the  three  steps  used 
in  squaring  a  number  by  cross  multiplication,  with  which 

(VIII-12) 


process  the  pupils  are  entirely  familiar;  this  is  by  far  the 
simplest  and  most  readily  comprehended  explanation  of 
this  difficult  operation.  Show  the  processes  of  squaring  by 
cross  multiplication  and  of  extracting  the  square  root  side 
by  side  and  step  for  step  on  the  ])lackboard,  for  form  and 
relation.  Use  drawings  for  a  clearer  understanding  and  for 
illustration.    Show  that  squaring  the  root  proves  the  work. 


Exercise  22 

—Written. 

Call  for  Proofs 

Answers: 

1.  13 

6.  41 

;            11.  35; 

2.  12 

7.  70 

12.  67; 

3.  23 

8.  18 

13.  56; 

4.  14 

9.  32 

14.  98. 

5.  25, 

10.  83 

Exercise  24 

—Written. 

Call  for  Proofs 

Answers : 

1. 

15.;        5. 

819.; 

9.  31.622+; 

2. 

35.;        6. 

1.18; 

10.     6.708+ . 

3. 

125.;        7. 

3.952 

-f; 

4. 

53.;        8. 

1.414 

+  ; 

Exercise  25 

—Written. 

Call  for  Proofs. 

Answers: 

1.  4i; 

6. 

17  in.; 

2.    A; 

7. 

6  yd.; 

3.  1.224+ ; 

8. 

22  yd.; 

4.21; 

9. 

1,008  boards; 

5.     .88 

1  +  ; 

10. 

17,576  cu.  in. 

Lesson  12 

This  method  is  fast  becoming  popular.    Be  sure  the  child 
chooses  very  carefully  his  approximate  divisor  even  into 

(VIII-13) 


hundredths,  so  he  may  have  an  accurate  answer  through 
hundredths.  He  may  be  glad  to  use  this  method  when  he 
handles  small  powers  or  products.    Some  children  do. 


Exercise  26— Written 

. 

Call  for  Proofs 

Answers: 

1.  83 

6.  56; 

11. 

1.73+ 

2.  67 

7.  98; 

12. 

1.41  + 

3.  41 

8.  23; 

13. 

2.24- 

4.  32 

9.     2.^ 

5;         14. 

3.16+ 

5.  35 

10.     3.5;         15. 

3.46+. 

Exercise  27- 

-Written 

. 

Call  for  Proofs. 

Answers: 

Time  Carefulhj 

1. 

264,667 

;          13. 

10,350; 

2. 

184,178 

14.  < 

360,498; 

3. 

84,943 

15. 

62,452; 

4. 

209,352 

16. 

1,380  and  5  rem.; 

5. 

272,313 

17. 

252; 

6. 

11,737 

18. 

5,161; 

7. 

35,376 

19. 

722  and  16  rem.; 

8. 

33,558 

20. 

909  and  5  rem. ; 

9. 

6,625 

21. 

819; 

10. 

17,928 

22. 

35; 

11. 

60,0'; 

^3; 

23. 

1.18; 

12.  6,200,064: 
Give  your  '^ class  honor"  now  for  work  in  powers  and  roots. 


EQUATIONS 
Note  Regarding  Grading. 

Where  Lessons  13  to  15  have  been  taught  in  the  seventh 
year,  they  must  nevertheless  now  be  given  in  their  entirety 
as  review  work  with  such  saving  in  time  as  is  made  possible 
by  the  previous  teaching. 

(VIII-14) 


Lessons  13  to  15 

This  work  is  to  be  gradually  developed  as  outlined  in 
the  text.  Care  must  be  taken  to  see  that  each  step  is 
mastered  before  the  next  one  is  attempted. 

Drill  most  carefully  on  transposition  and  the  accompany- 
ing changing  of  signs. 

If  necessary,  turn  back  to  these  lessons  in  a  short  time 
and  review  them. 

Have  the  children  use  the  equation  from  now  on  wherever 
it  will  save  time  or  simplify  the  work. 

Exercise  31 — Written.  Call  for  Proofs. 

Answers: 

1.  50  yd.;  7.      8  ft.; 

2.  13  oz.;  8.     12  ft.  by  15  ft.; 

3.  5A  min.  after  1  o'clock;      9.  100  ft.  by  125  ft.; 

4.  32  ft.;  10.     12  ft.  high; 

5.  18;  10  ft.  wide; 

6.  10  and  12;  15  ft.  long. 

If  you  have  not  yet  repeated  the  intelligence  test  given 
at  the  beginning  of  the  year,  now  is  a  good  time  to  do  so. 

MENSURATION 

Lesson  16 
Note  Regarding  Grading. 

Where  Lesson  16  has  been  taught  in  the  seventh  year,  it 
must  nevertheless  now  be  given  as  review  work  with  such 
saving  in  time  as  is  made  possible  by  the  previous  teaching. 

Teach  this  lesson  in  three  parts: 

(a)  That  the  square  on  the  hypotenuse  is  equal  to  the 

sum  of  the  squares  on  the  two  legs. 
(6)  That  since  the  square  on  the  hypotenuse  is  equal  to 
the  sum  of  the  squares  on  the  two  legs,  there- 
(VIII-15) 


fore,  the  square  on  the  hypotenuse  minus  the 
square  on  either  leg  equals  the  square  on  the 
other  leg. 
(c)  That  when  we  know  the  square  on  any  side  of  a 
triangle,  we  find  the  length  of  that  side  by 
extracting  the  square  root. 

Exercise  32 — Oral. 

Let  the  children  run  the  oral  work — you  will  readily  see 
where  any  weakness  lies — then  come  in  and  help. 


Exercise  33 — Written. 

Answers: 

1.     25  ft.; 

9. 

28.28+  ft.; 

2.     76  ft.; 

10. 

176.77+  ft.; 

3.     18  in.; 

11. 

23.58+  yd. 

4.     10  ft.; 

12. 

53.15+  ft.; 

6.       7.07+ 

in.; 

13. 

57.21+  ft.; 

7.  240  ft.; 

14. 

729.  cu.  in. 

8.  127.27+ ft.; 

Lesson  17 

It  is  of  vital  importance  that  the  pupil  should  understand 
that  every  equilateral  triangle  and  every  isosceles  triangle  can 
be  divided  into  two  right  triangles.  Teach  them  to  diagram 
all  of  their  work — in  some  cases  insist  on  drawings  carefully 
made  to  scale  with  ruler — in  some  cases  insist  on  pencil 
sketches  made  without  ruler  and  possibly  only  roughly 
approximating  scale,  but  drawn  and  marked  to  show  the 
proper  locations  and  lengths  of  the  known  dimensions  to 
facilitate  the  determining  of  the  unknown.  Do  this,  using 
simple  numbers  or  measurements  until  the  principle  is 
learned;  many  easy  ones  will  fix  the  rule.  Compare,  for 
children  apothem  in  polygon  with  altitude  in  triangle. 

(VITI-16) 


Exercise  34 — Oral. 

Let  the  children  run  it. 

Exercise  35 — Written. 

Answers: 

1.       5  ft.; 

6.     21.65  in.; 

2.     24  ft.; 

7.  173.2+  sq.  in.; 

3.     12  sq.ft.; 

8.     41.5+  sq.  in.; 

4.  432  sq.  ft. ; 

9.     93.528  sq.  in. ; 

5.      8.66+ in.; 

10.  201.24  sq.  in. 

.866+  in. 

for  each  1  in.  of  side; 

Lesson  18 

Make  certain  that  the  pupils  understand  that  similar 
triangles  may  occupy  different  positions  without  affecting 
their  similarity.  This  is  clearly  demonstrated  by  reference 
to  Figure  7  which  is  composed  of  the  triangles  shown  in 
Figures  4  and  5,  and  that  these  are  similar  is  proven  by 
Figure  6. 

A  practical  demonstration  of  this  method  of  making 
measurements  by  laying  out  triangles  in  a  near-by  field  is 
of  great  value  and  interest  to  the  pupils  and  should  be 
undertaken  if  conditions  permit.  Problem  projects  are 
plentiful  here;  teach  how  to  clear  of  fractions  by  reducing 
to  L.  C.  D.    Make  use  here  of  algebraic  equations. 

Exercise  37 — Written. 
Answers: 

1.  55  ft.;  4.  885  ft.; 

2.  64  ft.;  5.     30  in.; 

3.  156  ft.  3  in. ;  6.     22  ft.  6  in. 

Lesson  19 

Protractor  must  be  made  or  bought. 
(VUI-17) 


Lesson  20 

In  this  lesson  we  show,  for  the  first  time,  that  the  area 
of  a  circle  equals  ttR^.  Spare  no  effort  to  have  this  clearly 
understood.     Let  him  substitute  what  he  knows  and  he 

will  see  that  —  =  ttR^. 
2 

Finding  the  length  of  an  arc  or  the  area  of  the  sector  of  a 
circle  is  merely  the  combining  of  several  processes  which 
the  pupil  has  previously  learned,  and  should  offer  no 
difficulty.  Call  attention  to  the  fact  that  an  arc  is  measured 
along  the  curved  line  and  that  this  cannot  be  done  with  a 
ruler. 

Select  pupils  across  the  room,  say  those  in  seat  3  in  each 
row,  to  do  the  questioning.  Tomorrow  give  those  in  seat  4 
a  chance,  and  so  on. 

Use  the  equation  form  wherever  possible. 

Exercise  41 — Written. 


Answers: 

1. 

L5708yd.; 

10. 

8  ft.; 

•2. 

2.0944  ft.; 

11. 

2  ft.; 

3. 

6iin.; 

12. 

25  ft.; 

4. 

4  in.; 

13. 

40°; 

5. 

62.832  ft.; 

14. 

180°; 

6. 

12.5664  sq.  ft.; 

15. 

628.32  yd.; 

7. 

58.905  sq.  ft.; 

16. 

20  yd.; 

8. 

981.75  sq.  yd.; 

17. 

31.416  yd. 

9. 

19.635  sq.  in.; 

Note  Regarding  Grading. 

Where  Lessons  21  to  24  have  been  taught  in  the  seventh 
year,  they  must  nevertheless  now  be  given  in  their  entirety 
as  review  work  with  such  saving  in  time  as  is  made  possible 
by  the  previous  teaching. 

(VIII-18) 


Lesson  21 

Do  not  proceed  until  you  are  certain  that  the  pupils 
understand  clearly  what  is  meant  by  the  slant  height,  the 
altitude,  the  lateral  area,  and  the  entire  area  of  a  pyramid. 

Show  that  the  slant  height,  the  altitude  and  a  line  joining 
these  two  at  the  base  form  a  right  triangle  of  which  the 
slant  height  is  the  hypotenuse.  Tell  them  to  play  it  is 
glass,  then  see  the  lines. 

Also  show  that  the  slant  height,  one  edge  of  the  pyramid, 
and  a  line  joining  these  two  at  the  base  form  a  right  triangle 
of  which  the  edge  of  the  pyramid  is  the  hypotenuse. 

Now  let  the  children  take  prisms  and  pyramids  and 
talk  ])efore  the  class.  Let  them  tell  all  they  know  about 
these  solids. 

The  child  must  be  shown  that  finding  the  area  of  a  lateral 
face  of  a  pyramid  is  nothing  more  than  finding  the  area  of 
a  triangle  and  this  he  already  understands. 

Exercise  42 — Oral  and  Written. 

Work  hard  to  get  imaging  all  the  time.  Make  them  see 
it  in  the  air. 

Demonstrate  that  the  volume  of  a  pyramid  is  ^  as  great 
as  the  volume  of  a  prism  having  the  same  altitude  and  base, 
and  the  child  will  have  no  difficulty  in  understanding  that: 
Area  of  base  X  Altitude  -j-  3  =  Volume. 

To  make  this  clear,  have  one  of  the  pupils  or  all  make  a 
prism  and  a  pyramid  of  same  dimensions,  both  with  open 
ends;  have  them  bring  sawdust,  salt,  or  sand.  Let  the 
child  fill  the  prism  using  the  pyramid  as  a  measure.  He  will 
see  that  it  takes  three  measures  full;  then  he  knows  that  a 
pyramid  holds  just  i  as  much  as  a  prism  of  the  same  measure- 
ments; if  he  gets  the  whole  thing  (prism)  first,  he  will  have 
rio  difficulty  with  the  pyramid. 

Be  ready  to  show  the  children  how  to  draw  a  prism,  a 
pyramid,  an  octagon,  etc.,  rapidly;    it  will  save  time  and 

(VIII-19) 


energy  both  for  you  and  for  the  pupils;    draw  according 
to  the  numbers  suggested: 


^^ ^> 


3 


Lines  drawn  from  the  apex  directly  to  the  center  of  the 
base  and  to  the  vertices  of  the  figure  desired,  form  a  pyra- 
mid.    Use  the  equation  form  wherever  possible. 

Exercise  43 — Construction  Work. 

Insist  on  each  child  making  one  of  each.    Use  salt,  sand, 
sawdust;  anything  to  compare  volumes. 

Exercise  44 — Written. 
Answers: 

1.  Volume,      1,500  cu.  ft.; 
Perimeter,       60  ft. ; 
Slant  Height,  21.36  ft.; 

2.  384sq.  in.; 

3.  Volume,         216.5+  cu.  in.; 
Slant  Height,  15.61+  in.; 

4.  927.6  sq.  ft.; 

5.  5,760  pieces; 

6.  120cu.  in.; 

7.  25  ft.; 

8.  25.29+  in.; 

9.  48  cu.  in. ; 

10.  Volume,      93,391,360  cu.  ft.; 
Slant  Height,         613.45+  ft.; 
Lateral  Area,  937,351+  sq.  ft. 

Lesson  22 

This  lesson  should  be  taught  in  the  same  manner  as 
Lesson  21  on  pyramids,  with  the  necessary  omission  of  those 

(VIII-20) 


remarks  which  do  not  apply  in  the  case  of  cones.    Use  the 
equation  form  wherever  possible. 

Exercise  46 — Written. 
Answers: 

1.  Area  of  base,  314.16  sq.  ft.;  5.     41.888  cu.  in.; 
Volume,       1,570.8  cu.  ft.;  6.  200  cu.  in.; 
Circumference, 62.832  ft. ;  7.     10  ft. ; 

Slant  height,     18.02  +  ft. ;  8.       5  ft. ; 

2.  301.59+  sq.  in.;    9.  301.59+  cu.  in.; 

3.  35.49+ in.;         10.      7i  in. 

4.  Volume,  197.92+  cu.  in.; 
Slant  height,    21.21+ in.; 

Lesson  23 

Finding  the  lateral  area  of  a  frustum  is  not  a  difficult 
process  (average  perimeter  X  slant  height).  Give  child 
drawings  of  a  trapezoid 


then     /  \       then 


nam 


so  he   will   see   that   average   perimeter  X  slant   height 
lateral  area. 


Exercise  48 — Written. 

Answers: 

1.  Area  of  side,     490.09-sq.  in.; 

5. 

4  in.; 

Area  of  bottom,  78.54    sq.  in. ; 

6. 

150  sq.  in.; 

Total  area,       568.63-sq.  in.; 

7. 

20  in.; 

2.  136  sq.  in.; 

8. 

11  ft.; 

3.  301.59+  sq.  in.; 

9. 

10  in.; 

4.  490.09-  sq.  in.; 

10. 

36  in. 

(VIII-21) 

Lesson  24 

Follow  the  text  carefully ;  illustrate  and  demonstrate 
wherever  possible;  avoid  permitting  the  pupils  to  memorize 
a  lot  of  formulae  which,  to  them,  are  meaningless — instead, 
show  how  each  formula  is  obtained  by  reasoning,  so  that  the 
pupil  can,  when  necessary,  reason  along  the  same  lines  and 
construct  his  own  formulae.  The  children  love  to  make  the 
demonstrations  given  in  the  text;  encourage  it,  for  in  no 
other  way  do  they  grasp  the  rules  so  quickly.  Ask  for 
letter  formulae  all  the  time  now. 


Exercise  50 — Written. 

Answers: 

1. 

Area  great  circle, 

314.16  sq.  in.; 

Area  curved  surface, 

1,256.64  sq.  in.; 

2. 

615.75-h  sq. 

ft; 

3. 

19.635  sq.  in.; 

4. 

201,062,400  sq.  mi.; 

5. 

$109.08; 

6. 

Area  great  circle,  3,141,600  sq.  mi.; 

Radius, 

1,000  mi.; 

Diameter, 

2,000  mi.; 

7. 

33i  cu.  in. 

8. 

113.1-  cu. 

in.; 

9. 

16.96+  in, 

10. 

Diameter,   7.07+  in 

Volume,  185.04+  cu 

I.  in. 

Give 

1  your  "class  honor" 

now  for  mensuration  work. 

Exercise  51 — Oral  Review. 

Use  letters  and  symbols  very  freely.  Hold  a  contest  on 
abbreviations  and  signs.     See  Part  VIII,  page  169. 

Let  the  addition  work  be  oral  and  watch  the  various 
grouping    methods   carefully.      Let  some   add    downward, 

(VIII-22) 


others  upward.  Stop  them  on  the  spot  to  correct  them — 
then  try  again.  Give  a  few  minutes  of  this  work  every 
day  now  without  fail. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 


Exercise  52 — Written  Review. 


More  review  work  of  a  similar  nature  may  be  given,  t 

luiiLting. 
Answers: 

1.       48.7; 

15. 

278,388 

29.     34,164 

2.  61,162,984.; 

16. 

234,367 

30.     32,923 

3.         H; 

17. 

316,932 

31.  343,744 

4.      25  ft.; 

18. 

348,208 

32.  391,329 

5.        6.92+ in.; 

19. 

682 

33.  382,046 

6.       12  in.; 

20. 

559 

34.  537,884 

7.       60°; 

21. 

783 

35.  302,632 

8.         5  in.; 

22. 

889 

36.  243,895 

9.      35.49+  in.; 

23. 

707 

37.  124,408 

10.       13.  in.; 

24. 

785 

38.     24,829 

11.     84,330; 

25. 

35,430 

39.  481,378 

12.  232,596; 

26. 

30,884 

40.  123,009 

13.  804,172; 

27. 

33,855 

41.  111,009 

14.  136,053; 

28. 

30,966 

42.  103,019. 

GRAPHIC 

CHARTS   ANL 

)   METERS 

Lesson  25 
This  lesson  will  prove  very  interesting  and  instructive  to 
the  pupils.  Encourage  them  in  constructing  graphs  when-' 
ever  the  opportunity  presents  itself.  Work  for  neatness 
and  for  comprehension  of  the  advantages  of  each  of  the 
several  ways  of  graphing.  Let  them  tell  how  various  things 
might  be  done. 

Problem  projects  can  be  used  to  advantage  here. 
(VIII-23) 


Exercise  54— Written. 

Answers: 

1.  Ratio    1  to  86; 

2.  Ratio  37  to    1; 

7.  New  England 25° 

Middle  Atlantic 76° 

East  North  Central 72° 

West  North  Central 47° 

South  Atlantic 47° 

East  South  Central 32° 

West  South  Central 36° 

Mountain 11° 

Pacific 14° 

United  States 360° 

8.  Dry  Goods 20%     72 

Furniture 50%  180' 

Carpets 17%    61° 

Curtains 5%     18' 

Miscellaneous 8%     29 

Total  Sales 100%  360^ 


Lesson  26 

The  ability  to  read  meters  and  compute  gas  and  electric 
bills  correctly  may  save  the  pupils  many  dollars  in  later 
years.  Teach  both  subjects  thoroughly.  If  you  can  get 
a  discarded  electric  meter  from  the  local  power  company 
it  will  help  a  lot.  Use  problem  projects.  Have  different 
"gas  men"  chosen  from  class;  keep  active  readings  going 
on;  call  on  different  pupils  right  along;  if  they  miss,  call 
.on  them  again  soon  after  till  they  learn  how.  In  going  to 
the  "Gas  Office/'  let  some  complain  about  their  bills;  let 
others  be  officials  and  work  it  out  for  them  in  detail  if 
need  be;   they  love  to  do  that. 

Explain  carefully  the  meaning  of  "kilowatt  hour"  and 
its  abbreviation,  "k.  w.  hr." 

(VIII-24) 


Exercise  56 — Written. 


Answers: 

1.  $2.40;  6.  Gross  $6.36 

2.  $2.16;  Net     $5.34 

3.  Gross    $4.68;  7.  $1.65 
Net       $4.38;           8.  Gross  $1.62 

4.  Gross  $15.24;  Net     $1.44 
Net     $14.94 

5.  Gross    $7.80 
Net       $6.60 

Give  your  "class  honor"  now  for  chart  and  meter  work. 

PERCENTAGE 
Lesson  27 
The  advantages  of  the  method  shown  over  the  tedious 
process  of  hsting  each  partial  payment  are  self-evident. 
This  method  is  so  simple  that  the  interest  on  almost  any 
installment  account  can  be  computed  without  the  use  of 
paper  and  pencil.  This  is  vital  to  every  child.  The  world 
does  not  know  how  much  is  lost  through  ignorance  regard- 
ing this  subject.  Use  problem  projects.  Let  them  run  an 
installment  furniture  house.  Let  some  go  there  to  buy 
furniture,  then  have  them  make  their  monthly  payments, 
and  after  computing  the  interest  have  them  settle  their 
accounts. 


Exercise  58 — Written 

Answers: 

1.      $4.55 

5.        $60.92 

9.  $11,550.00; 

2.  $637.50 

6.        $44.00 

10.           $5.60. 

3.     $21.38 

7.  $1,243.75 

4.       $1.15 

8.         $5.28 

Note:  Do  not  forget  the  oral  drill  on  rapid  addition. 
(VIII-25) 


Lesson  28 
Note  Regarding  Grading. 

Where  Lesson  28  has  been  taught  in  the  seventh  year,  it 
must  nevertheless  now  be  given  as  review  work  with  such 
saving  in  time  as  is  made  possible  by  the  previous  teaching. 

When  a  note  bearing  interest  is  discounted,  the  two  inter- 
est calculations  must  be  kept  entirely  separate.  First  find 
\sihat  the  note  and  interest  will  amount  to  at  maturity, 
then  discount  this  total  amount  for  the  required  time. 
Explain  one  problem  very  carefully;  leave  the  work;  have 
children  who  wish  to  learn  ask  questions  about  the  work, 
or  point  out  what  they  do  not  understand.  Encourage 
questions,  then  go  ahead.  Use  problem  projects.  Let 
them  have  a  bank  window  in  room  and  go  there  to  ha\e 
notes  discounted,  some  without  interest  others  with  interest. 
It  will  ''liven"  it  up. 

Exercise  60 — Written. 

Answers: 

1.  S394.00; 

2.  $347.08 

3.  $1,499.40 

4.  $282.07 


6.  $400.00;  9.  $350.00; 
90  days;  10.  $360.00; 

7.  $240.00;  11.  $900.00. 

5% 


5.      $818.69;        8.  $510.20; 

Lesson  29 

It  will  be  noted  that  mortgages  and  bonds  are  treated  in 
one  lesson  and  that  attention  is  called  to  the  fact  that 
stocks  are  never  to  be  confused  with  bonds.  Lay  particular 
stress  on  this  distinction  which,  unfortunately,  is  known  by 
far  too  few  people.  Mortgages  and  bonds  are  closely  related 
as  a  bond  is  really  a  part  of  a  mortgage. 

Use  problem  projects.  Let  different  children  represent 
the  various  parties  to  a  mortgage  and  carry  out  a  transaction 
in  detail,  even  to  the  recording  of  the  ''satisfaction." 

(VIII-2(>) 


Exercise  62 — Written. 


ns^ 

ivers: 

1. 

$2,375.00 

5. 

(a)  Dec.  1 

1925, 

$40,000.00 

2. 

$2,286.00 

Dec.  1 

1926, 

$60,000.00 

3. 

$1,320.00 

Dec.  1 

1927, 

$100,000.00 

4. 

$4,350.00 

(h)  June  1 

1921, 

$6,000.00 

Dec.  1 

1925, 

$6,000.00 

June  1 

1926, 

$4,800.00 

Dec.  1 

1926, 

$4,800.00 

Dec.  1 

1927, 

$3,000.00 

(c) 

$75,600.00 

6. 

$7.50 

Lesson  30 

Here,  again,  pains  must  be  taken  to  emphasize  the  dis- 
tinction between  (a)  bonds  and  stocks,  (6)  bondholders  and 
stockhoklers,  (c)  interest  and  dividends. 

Organize  a  corporation  in  your  school  room  and  have  it 
represent  a  successful  enterprise  for  a  time,  then  an  unsuc- 
cessful one,  that  the  pupils  may  better  visuahze  the  fate 
of  an  investor  in  ''wild  cat"  securities.  The  problem 
project  will  give  the  children  a  most  thorough  comprehension 
of  this  subject. 


Exercise  64 — Written. 

Answers: 

1.                   7i%; 

6.     $38,500.00; 

2.                   5%; 

7.             20%; 

3.        $23,000.00; 

8.                2i% 

4.  $1,000,000.00; 

9.          $500.00; 

5.        $24,000.00; 

10.  $121,000.00; 

55  shares. 

Note:  Remember  the  addition  drill- 
more  speed. 

(VIII-27) 


-urge  for  more  and 


Lesson  31 

After  disposing  of  the  preliminary  work  covered  by  this 
lesson,  the  actual  computation  of  yield  must  be  very  care- 
fully undertaken.  Every  man  and  woman  should  be  able 
to  compute  the  percentage  of  income  on  a  contemplated 
investment  without  depending  upon  the  statements  of 
salesmen  and  others  who,  themselves,  seldom  are  correctly 
informed.  Lay  stress  upon  the  advantages  to  be  gained  by 
those  who  know  how  to  invest  their  savings  properly. 

Example  #1  is  illustrative  of  a  case  where  stock  is  bought 
at  a  discount  and  held  as  a  permanent  investment;  in  such 
cases  it  must  always  be  assumed  that  the  market  value  of 
the  stock  remains  unchanged,  for  no  cognizance  can  be  taken 
of  any  change  in  the  market  value  until  such  time  as  the 
stock  is  actually  disposed  of;  therefore,  the  percentage  of 
income  must  be  computed  on  the  basis  of  the  cost  price. 

Examples  #2  and  #3  show  bonds  bought  at  a  discount 
and  at  a  premium  respectively.  As  every  bond  is  worth  its 
par  value  at  maturity,  the  discount  or  premium  must  be 
distributed  over  the  life  of  the  bond.  Thus,  the  value  of 
the  bond  changes  proportionately  from  year  to  year  as  the 
date  of  maturity  approaches;  therefore,  the  percentage  of 
income  must  be  computed  on  the  basis  of  the  average  value; 
that  is,  the  value  which  is  half  way  between  the  purchase 
price  and  the  par  value.  Go  slowly  but  surely  here.  Talk 
it  over  with  the  children  and  let  them  ask  for  help  freely. 

Examples  #4  and  #5  show  stocks  which  were  sold  for 
more  and  less  respectively  than  what  was  paid  for  them. 
In  cases  of  this  kind,  the  gain  or  loss  is  distributed  over 
the  period  during  which  the  stock  was  owned,  and  the 
percentage  of  income  must  be  computed  on  the  basis  of  the 
average  value;  that  is,  the  value  which  is  half  way  between 
the  purchase  price  and  the  selling  price.  Continue  the 
project  (Exercise  65) ;  let  each  child  buy  some  stock  at  par 
and  market  value.     Then  watch  the  yield. 

(VIII-28) 


Exercise  67 — Written. 


Answers: 

1.  $4,432.50; 

6.  6t^A%; 

2.    40  shares; 

7.  4/A%; 

3.     10f%  on  1  share; 

8.  5tVo%; 

10f%  on  15  shares; 

9.  The  stock  is  i  of  1% 

4.         66if; 

more  profitable; 

5.           90  shares; 

10.  6^%; 

133^; 

11.  8^%. 

$12,000.00; 

Lesson  32 

If  the  child  can  be  made  to  realize  the  value,  to  him,  of 
a  thorough  knowledge  of  insurance  matters,  this  lesson  will 
be  much  more  thoroughly  and  quickly  mastered  than  if  it 
is  approached  from  a  purely  arithmetical  standpoint. 
I  Each  class  of  insurance  should  be  discussed  separately 
and  the  examples  relating  thereto  should  then  be  worked. 

Run  over  the  first  part  rapidly.  When  you  take  up  the 
Insurance  Office  Project,  let  children  vie  with  each  other 
to  find  out  things;  asking  pointed  questions — watching 
papers;  i.  e.,  getting  right  papers,  correct  names,  etc. 
See  that  your  officials  are  well  posted.  Give  them  policies  to 
study  and  give  them  reference  books  so  they  may  be  a 
fountain  head  of  knowledge. 

Exercise  70 — Written. 
Answers: 

1.  $29.01; 

2.  (a)  $4,925.00  premium; 
lb)  $5,000.00  collected; 
(c)   Age  45; 

3.  (a)  $7,650.00  premium; 

(6)  $10,000.00  paid  to  beneficiary; 
(c)   Int.  on  $10,000.00  for  10  years  =  $6,000.; 
(VIII-29) 


4.  $180.00; 

5.  (a)  Manufacturer  gained  $1,500.00; 

(b)  Bonding  company  lost  $1,500.00; 

6.  (a)  Employer  gained  $25,625.00; 

(6)  Insurance  company  lost  $25,625,00; 

(c)  Accident  cost  employer  $15,860.00; 

(d)  Accident  cost  insurance  company  $30,000.00. 

Give  j/our  "class  honor"  now  for  percentage  work. 

Exercise  71 — Oral  Review. 

Give  plenty  of  drill  on  addition — watch  the  slow  ones 
most — make  ttiem  see  the  groups.  They  cannot  take  their 
own  time  about  it  if  the  work  is  oral — let  them  compete 
to  see  who  finds  the  most  groups  and  who  adds  most  rapidly. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 

Exercise  72 — Written  Review. 


More  review  work  of  a  similar  nature 

;  may  be  give 

permitting. 

Answers: 

1.  10°  14'  32"; 

11.           28 

2.  (a)       2,304; 

12.           53 

(b)  262,144; 

13.           72 

3.  (a)         819; 

14.         526 

(b)             4i; 

15.         718 

4.  28.28+  ft.; 

16.         643 

5.     2fft.; 

17.  133,425 

6.  29.45+  sq.  in.; 

18.  291,788 

7.  Volume,    3,840  cu.  ft.; 

19.  392,290 

Slant  height,  23.32+  ft.; 

20.  147,467 

8.          $76.00; 

21.  774,917 

9.        $676.00; 

22.  408,165 

10.          5tVo%; 

23.  265,202 

(VIII-30) 

34. 

151,632 

35. 

363,552 

36. 

360,372 

37. 

41,630 

38. 

32,560 

39. 

33,115 

40. 

27,910 

41. 

42,705 

42. 

27,733 

24.  90,263 

25.  381,344 

26.  316,989 

27.  322,075 

28.  178,415 

29.  333,717 

30.  478,928 

31.  345,400 

32.  251,228 

33.  255,645 

PARTNERSHIP 
Lesson  33 
Let  several  children  impersonate  the  partners  in  some  of 
the  examples  to  see  if  they  agree  on  the  division  of  their 
profit,  etc.  Be  sure  they  notice  if  investments  are  equal  or 
unequal.  Lead  the  child  to  be  on  the  alert  for  the  wording 
that  tells  the  story. 

Problem  projects  are  plentiful  here. 

Exercise  73 — Oral. 

Divide  room  into  groups — A,  B  or  A,  B,  C.  Keep  each  one 
asking  questions  and  watching  his  profits.  Interest  will  be 
red  hot. 

Exercise  74 — Written. 
Answers: 


1. 

Johnson,     $5,307.00 
Brown,        $3,538.00 

4. 

A's  profit,  $4,510.00; 
B's  profit,  $3,690.00; 

2. 

Alexander,  $1,246.80 
Wilson,       $1,090.95 

5. 

A  39%;  B  36%; 
C  25%; 

Hendricks,     $779.25, 

6. 

$48,000.00; 

3. 

(Encourage  accurate  long 

7. 

X  withdrew  $400.00; 

division) 

Y  invested    $400.00. 

Black,          $4,749.03; 

White,         $3,885.57 

) 

(VIII-31) 


Exercise  75 — Written. 

Answers: 

1.  A 

B 

C 


2. 
3. 
4. 
5. 


withdrew  8804.00 
invested  $804.00 
invested  $4,020.00 
$4,000.00 
$2,000.00 


6.  $666.67 

7.  $3,373.33: 

8.  $2,353.33: 
■  9.  $2,273.34; 
10.  No  balances. 


Give  your  ''class  honor"  now  for  partnership  work. 

Exercise  76 — Oral  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 


Exercise  77 — Written  Review. 

More  review  work  of  a  similar  nature  may  be  given,  time 
permitting. 
Answers: 


1. 

$16.61; 

16. 

21,312 

2. 

314.16  sq.  in.; 

17. 

43,772 

3. 

12.72+  in.; 

18. 

28,224 

4. 

4  in.; 

19. 

81,732 

5. 

5  p.  M.; 

20. 

54,612 

6. 

$492.50; 

21. 

341,999 

7. 

10.39+ in.; 

22. 

234,522 

8. 

$8.55; 

23. 

99,944 

9. 

68.1; 

24. 

484,471 

10. 

40.06  yd.; 

25. 

928 

11. 

$2,334,800,000.00; 

26. 

589,052 

12. 

(a)  SStu%  approximately ; 

27. 

411,825 

(b)  33i%; 

28. 

8,976 

(c)   37+%; 

29. 

437 

13. 

49,032; 

30. 

43,924 

14. 

15,066; 

31. 

60,898 

15. 

17,204; 

32. 

105,839 

(VIIT-32) 


33.  297; 

36.  913;        39.  437,433; 

42.     71,904 

34.  412; 

37.  725;        40.     64,715; 

43.  155,237 

35.  527; 

38.  248;        41.  440,187; 
General  Review 

44.  209,355, 

All  work  for  general  review  purposes  should  be  selected 
from,  or  based  on,  the  various  exercises  which  constitute  the 
year's  work  in  the  text  book.    . 

Give  your  review  work  in  three  parts;   viz. : 
(a)  Oral  work  on  principles,  etc„ 
(5)   Oral  problems. 
(c)   Written  problems. 
Now  repeat  the  intelligence  test  given  at  the  beginning 
of  the  year,  and  give  each  pupil  his  record  for  the  tests  given 
in  Parts  V  to  VIII. 

Special  Intelligence  Test  in  Arithmetic 

The  following  10  problems  are  taken  from  a  series  of  22 
problems  prepared  as  an  Intelligence  Test  in  Arithmetic  for 
College  Freshmen  and  High  School  Seniors  by  Dr.  L.  L. 
Thurstone,  Division  of  Psychology,  Carnegie  Institute  of 
Technology,  Pittsburgh,  Pa.,  to  whom  we  herebj^  acknowl- 
edge our  indebtedness  for  their  use. 

The  time  allowed  for  the  solving  of  the  entire  series  of 
22  problems  is  30  minutes;  the  pro  rata  time  which  should 
be  allowed  for  the  solving  of  the  following  10  problems  is 
about  14  minutes,  but  considering  the  fact  that  your  pupils 
are  much  younger,  it  will  be  interesting  to  note  how  many 
of  the  pupils  can  solve  the  10  problems  in  30  minutes. 
Each  problem  is  within  the  scope  of  the  child's  education. 

If  facilities  are  at  hand,  papers  containing  the  problems 
should  be  prepared  in  advance  and  given  to  the  pupils  at 
the  proper  time;  otherwise  the  problems  should  be  written 
on  the  board  during  the  pupils'  absence  and  kept  covered 
until  the  proper  moment. 

(VIII-33) 


The  Problems: 

1.  A  firm   builds  a  warehouse  four  stories  high.     The 

interior  dimensions  of  the  building  are  50  by  200  ft. 
How  many  square  feet  of  floor  space  have  they 
provided  for  themselves? 

2.  If  concrete  curbing  and  gutter  on  a  street  cost  65  cents 

per  running  foot,  what  is  the  cost  of  the  curbing  and 
gutter  on  both  sides  of  a  city  block  500  ft.  long? 

.'•^^    3.   See  Figure   1.     This  figure  is  a 
^„  ^^^  cross  section  of  an  iron  gutter 

^  to  be  made  by  a  tinsmith.    It 

>^  is  made  by  bending  a  piece  of 

***  material  of  the  proper  width. 

3^  "  How  wide  must  the  material 

Figure  1  be? 

4.  If  a  steel  rail  weighs  60  lb.  per  yard,  how  many  tons 
of  rail  will  be  required  to  lay  \  mile  of  single-track 
railroad? 

5.  Calculate  the  weight  of  a  steel  plate  one  foot  square, 
\"  thick  with  a  rectangular  hole  which  measures 
3"X  8".     Steel  weighs  0.3  pound  per  cubic  inch. 

6.  A  contractor  offers  to  lay  an  asphalt  pavement  at 
$3.60  per  square  yard.  The  street  is  50  ft.  wide. 
How  much  must  the  lot  owners  on  both  sides  of  the 
street  be  assessed  for  each  foot  in  the  width  of  their 
lots? 

7.  A  tank  of  water  is  being  drained  at  the  rate  of  two 
cubic  feet  of  water  per  second  and  supplied  at  the 
rate  of  one  cubic  foot  per  second.  After  two  minutes 
there  are  one  hundred  cubic  feet  of  water  in  the  tank. 
How  much  water  was  in  the  tank  before  the  pipes 
were  opened? 

8.  What  must  be  the  length  of  a  bolt  under  the  head  to 
go  through  9^"  thickness  of  plank  and  allow  \\^ 
outside  for  taking  a  nut? 

(VIII-34) 


9.  What  will  be  the  expense  for  a  cement  sidewalk  on 

the  two  sides  of  a  corner  lot  50  ft.  by  100  ft.  if  the 

walk  is  5  ft.  wide  and  costs  10  cents  per  square  foot? 

10.  What  is  the  area  of  the  surface  of  a  boiler  plate  3'  9" 

by  1'  6*?     (Give  your  answer  in  square  feet.) 


:he 
1. 

Answers: 
50,000  sq.  ft.     (This  answer  includes  10,000  sq.  ft.  in 

basement,  and  makes  no  allowance  for  stairways,  etc.) 

2. 

$66qg)0; 

3. 

17  in.; 

4. 

52.8  tons  of  rail; 

5. 

18  1b.; 

6. 

SIO.OO; 

7. 

220cu.  ft.; 

8. 

lOfiin.; 

9. 

$77.50; 

10. 

of  sq.  ft. 

Examinations  (K  Desired) 

That  the  examinations  (if  desu-ed)  may  be  a  thorough 
test  of  the  pupil's  knowledge  of  the  work  covered,  the 
questions  should  be  selected  from  the  various  exercises 
which  constitute  the  year's  work  in  the  text  book,  but  the 
teacher  may  introduce  other  examples  of  a  similar  nature. 
Examinations  should  be  held  in  oral  as  well  as  in  written 
arithmetic,  and  should  test  the  pupil's  knowledge  of  both 
theory  and  application. 

A  Suggestion 

Show  the  weak  ones  why  and  where  they  failed;  see  if 
you  cannot  encourage  them  to  do  a  little  reviewing  in  their 
spare  time.  Perhaps  they  did  not  care  before  now  but 
are  just  beginning  to  realize  their  plight — a  word  of  encour- 
agement may  mean  everything  to  their  future  welfare — 
try  anyway,  it  can  do  no  harm. 

(VIII-3o) 


Teacher's  Memoranda 


(;,aylord  Bros. 

Makers 

Svraciise,  N.  Y. 

PAT.  JAN.  21,  1908 


YB  35864 


464670 


J- 


^^ 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


